Prime forms involving Repunits, R_n.

Thu Oct 21 19:26:06 CEST 2004

Et al,

	Here is where we are today. All of the sequences below have been tested to an 
exponent of five thousand. I have changed all titles to the use of R_n in place
of (10^n-1)/9. The second definition, which is shorter, I put it into the first
%Comment line. This is the second half of the sequences that I mailed out a week
ago last Thursday 14 October 2004.

	I found that the web site of Prof. Kamada at
http://homepage2.nifty.com/m_kamada/math/ to be most helpful.

the index should have a category for:

Prime forms involving Repunits, R_n.
	 X*10^n+Y*Repunits (X,Y)=1, X&Y belong to {d} d being the digits 1..9.

A004023, A056698, A089147, A002957, A056700, A056701, A056702, A056703, A056704, 
A056705, A056706, A056707, A056708, A056712, A056713, A056714, A056715, A056716, 
A056717, A056718, A056719, A056720, A056721, A056722, A056723, A056724, A056725, 
A056726, A056727.

The 29 forms, X*10^n+Y*Repunits, (X,Y)=1,
		X&Y belong to {d} d being the digits 1..9.  in lexiconal order.

Form 111...111
%I A004023 M2114
%S A004023 2,19,23,317,1031,49081,86453
%N A004023 Prime "repunits": 11...111 = (10^n - 1)/9 is prime.
............
%H A056698 M. Kamada, <a 
href="http://homepage2.nifty.com/m_kamada/math/11111.htm">Factorizations of 
11...11 (Repunit)</a>
............
%Y A004023 See A004022 for the actual primes.
%K A004023 hard,nonn,nice
%O A004023 1,1
%A A004023 njas

Form 133..333
%I A056698
%S A056698 1,15,41,83,95,341,551,669,989,1223,6923
%N A056698 Numbers n such that 10^n + 3*R_n is prime, where R_n = 11...1 is the 
repunit (A002275) of length n.
%C A056698 Also numbers n such that (4*10^n-1)/3 is prime.
%H A056698 M. Kamada, <a 
href="http://homepage2.nifty.com/m_kamada/math/13333.htm">Factorizations of 
133...33</a>
%t A056698 Do[ If[ PrimeQ[ 10^n + 3*(10^n-1)/9], Print[n]], {n, 0, 30470}]
%K A056698 hard,nonn
%O A056698 0,2
%A A056698 Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 10 2000

Form 177..777
%I A089147
%S A089147 1,3,9,13,42,51,54,91,120,168,510,819,1071,1756,3010,4333
%N A089147 Numbers n such that 10^n + 7*R_n is prime, where R_n = 11...1 is the 
repunit (A002275) of length n.
%C A089147 Also numbers n such that (16*10^n-7)/9 is prime.
%H A089147 M. Kamada, <a 
href="http://homepage2.nifty.com/m_kamada/math/17777.htm">Factorizations of 
177...77</a>
%t A089147 Do[ If[ PrimeQ[10^n + 7(10^n - 1)/9], Print[ n]], {n, 7000}]
%Y A089147 For the primes see A088465.
%K A089147 base,nonn
%O A089147 1,2
%A A089147 Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 05 2003

Form 199..999
%I A002957 M0680
%S A002957 1,2,3,5,7,26,27,53,147,236,248,386,401,546,785,1325,1755,2906,3020,
%T A002957 5407,5697,5969,7517
%N A002957 Numbers n such that 2*10^n - 1 is prime.
%N A002957 Also numbers n such that 10^n + 9*R_n is prime, where R_n = 11...1 is 
the repunit (A002275) of length n.
%D A002957 H. Riesel, "Prime numbers and computer methods for factorization," 
Progress in Mathematics, Vol. 57, Birkhauser, Boston, 1985, Page 162.
%D A002957 C. R. Zarnke and H. C. Williams, Computer determination of some large 
primes, pp. 563-570 in Proceedings of the Louisiana Conference on Combinatorics, 
Graph Theory and Computer Science. Vol. 2, edited R. C. Mullin et al., 1971.
%H A002957 M. Kamada, <a 
href="http://homepage2.nifty.com/m_kamada/math/19999.htm">Factorizations of 
199...99</a>
%t A002957 Do[ If[ PrimeQ[ 2*10^n - 1], Print[n] ], {n, 1, 15000} ]
%K A002957 hard,nonn
%O A002957 1,2
%A A002957 njas, Simon Plouffe (plouffe(AT)math.uqam.ca)
%E A002957 Corrected and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 02 
2001.
%E A002957 Other known primes: 15749, 19233, 38232, 55347.

Form 211..111
%I A056700
%S A056700 2,3,12,18,23,57,128,543,584,833,2450,2810,2873,3671,6384
%N A056700 Numbers n such that 2*10^n + R_n is prime, where R_n = 11...1 is the 
repunit (A002275) of length n.
%C A056700 Also numbers n such that (19*10^n-1)/9 is prime.
%H A056700 M. Kamada, <a 
href="http://homepage2.nifty.com/m_kamada/math/21111.htm">Factorizations of 
211...11</a>
%t A056700 Do[ If[ PrimeQ[ 2*10^n + (10^n-1)/9], Print[n]], {n, 0, 10000}]
%K A056700 hard,nonn
%O A056700 0,1
%A A056700 Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 10 2000
%E A056700 6384 from Hugo Pfoertner (hugo(AT)pfoertner.org), Oct 16 2004

Form 233..333
%I A056701
%S A056701 0,1,2,3,4,10,16,22,53,91,94,106,138,210,282,522,597,1049,2227,6459,
%T A056701 10582
%N A056701 Numbers n such that 2*10^n + 3*R_n is prime, where R_n = 11...1 is the 
repunit (A002275) of length n.
%C A056701 Also numbers n such that (7*10^n-1)/3 is prime.
%H A056701 M. Kamada, <a 
href="http://homepage2.nifty.com/m_kamada/math/23333.htm">Factorizations of 
233...33</a>
%t A056701 Do[ If[ PrimeQ[ 2*10^n + 3*(10^n-1)/9], Print[n]], {n, 0, 15001}]
%K A056701 hard,nonn
%O A056701 0,3
%A A056701 Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 10 2000

Form 277..777
%I A056702
%S A056702 0,2,3,9,15,18,36,63,114,225,405,482,1241,2018
%N A056702 Numbers n such that 2*10^n + 7*R_n is prime, where R_n = 11...1 is the 
repunit (A002275) of length n.
%C A056702 Also numbers n such that (25*10^n-7)/9 is prime.
%H A056702 M. Kamada, <a 
href="http://homepage2.nifty.com/m_kamada/math/27777.htm">Factorizations of 
277...77</a>
%t A056702 Do[ If[ PrimeQ[ 2*10^n + 7*(10^n-1)/9], Print[n]], {n, 0, 6000}]
%K A056702 hard,nonn
%O A056702 0,2
%A A056702 Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 10 2000

Form 299..999
%I A056703
%S A056703 0,1,3,6,7,19,27,43,55,207,1311
%N A056703 Numbers n such that 3*10^n - 1 is prime.
%C A056703 Also numbers n such that 2*10^n + 9*R_n is prime, where R_n = 11...1 is 
the repunit (A002275) of length n.
%H A056703 M. Kamada, <a 
href="http://homepage2.nifty.com/m_kamada/math/29999.htm">Factorizations of 
299...99</a>
%t A056703 Do[ If[ PrimeQ[ 2*10^n + (10^n-1)], Print[n]], {n, 0, 3000}]
%K A056703 hard,nonn
%O A056703 0,2
%A A056703 Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 10 2000
%E A056703 Other known primes: 7050, 9439, 26044, 33058, 34507, 49314.

Form 311..111
%I A056704
%S A056704 1,2,5,10,11,13,34,47,52,77,88,554,580,1310,1505,8537
%N A056704 Numbers n such that 3*10^n + 1*R_n is prime, where R_n = 11...1 is the 
repunit (A002275) of length n.
%C A056704 Also numbers n such that (28*10^n-1)/9 is prime.
%H A056704 M. Kamada, <a 
href="http://homepage2.nifty.com/m_kamada/math/31111.htm">Factorizations of 
311...11</a>
%t A056704 Do[ If[ PrimeQ[ 3*10^n + (10^n-1)/9], Print[n]], {n, 0, 10000}]
%K A056704 hard,nonn
%O A056704 0,2
%A A056704 Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 10 2000

It was previously reported that in A056704 n=9439 also is prime. Hugo Pfoertner
found it to be composite with PFGW and I also found it to not be prime with
Mathematica.

Form 377..777
%I A056705
%S A056705 0,1,11,17,773,18155
%N A056705 Numbers n such that 3*10^n + 7*R_n is prime, where R_n = 11...1 is the 
repunit (A002275) of length n.
%C A056705 Also numbers n such that (34*10^n-7)/9 is prime.
%H A056705 M. Kamada, <a 
href="http://homepage2.nifty.com/m_kamada/math/37777.htm">Factorizations of 
377...77</a>
%t A056705 Do[ If[ PrimeQ[ 3*10^n + 7*(10^n-1)/9], Print[n]], {n, 0, 30070}]
%K A056705 hard,nonn
%O A056705 0,3
%A A056705 Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 10 2000

Form 411..111
%I A056706
%S A056706 1,3,13,25,72,108,375,393,589,973
%N A056706 Numbers n such that 4*10^n + 1*R_n is prime, where R_n = 11...1 is the 
repunit (A002275) of length n.
%C A056706 Also numbers n such that (37*10^n-1)/9 is prime.
%H A056706 M. Kamada, <a 
href="http://homepage2.nifty.com/m_kamada/math/41111.htm">Factorizations of 
411...11</a>
%t A056706 Do[ If[ PrimeQ[ 4*10^n + (10^n-1)/9], Print[n]], {n, 0, 10000}]
%K A056706 hard,nonn
%O A056706 0,2
%A A056706 Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 10 2000

Form 433..333
%I A056707
%S A056707 1,2,16,31,37,55,62,172,174,197,727,1246,1752,4318,4328,4930
%N A056707 Numbers n such that 4*10^n + 3*R_n is prime, where R_n = 11...1 is the 
repunit (A002275) of length n.
%C A056707 Also numbers n such that (13*10^n-1)/3 is prime.
%H A056707 M. Kamada, <a 
href="http://homepage2.nifty.com/m_kamada/math/43333.htm">Factorizations of 
433...33</a>
%t A056707 Do[ If[ PrimeQ[ 4*10^n + 3*(10^n-1)/9], Print[n]], {n, 0, 5000}]
%K A056707 hard,nonn
%O A056707 0,2
%A A056707 Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 10 2000

Form 477..777
%I A056708
%S A056708 1,4,13,25,36,357,373,1041,1089,1093,1297
%N A056708 Numbers n such that 4*10^n + 7*R_n is prime, where R_n = 11...1 is the 
repunit (A002275) of length n.
%C A056708 Also numbers n such that (43*10^n-7)/9 is prime.
%H A056708 M. Kamada, <a 
href="http://homepage2.nifty.com/m_kamada/math/47777.htm">Factorizations of 
477...77</a>
%t A056708 Do[ If[ PrimeQ[ 4*10^n + 7*(10^n-1)/9], Print[n]], {n, 0, 6000}]
%K A056708 hard,nonn
%O A056708 0,2
%A A056708 Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 10 2000

Form 499..999
%I A056712
%S A056712 2,3,4,6,14,54,210,390,594,3460
%N A056712 Numbers n such that 5*10^n-1 is prime.
%C A056712 Also numbers n such that 4*10^n + 9*R_n is prime, where R_n = 11...1 is 
the repunit (A002275) of length n.
%H A056712 M. Kamada, <a 
href="http://homepage2.nifty.com/m_kamada/math/49999.htm">Factorizations of 
499...99</a>
%t A056712 Do[ If[ PrimeQ[ 4*10^n + (10^n-1)], Print[n]], {n, 0, 4660}]
%K A056712 hard,nonn
%O A056712 0,1
%A A056712 Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 11 2000
%E A056712 Other known primes: 8072, 15796, 16131, 29282.

Form 511..111
%I A056713
%S A056713 0,5,12,15,84,144,150,1235,1727,1812,8687
%N A056713 Numbers n such that 5*10^n + R_n is prime, where R_n = 11...1 is the 
repunit (A002275) of length n.
%C A056713 Also numbers n such that (46*10^n-1)/9 is prime.
%H A056713 M. Kamada, <a 
href="http://homepage2.nifty.com/m_kamada/math/51111.htm">Factorizations of 
511...11</a>
%t A056713 Do[ If[ PrimeQ[ 5*10^n + (10^n-1)/9], Print[n]], {n, 0, 10000}]
%K A056713 hard,nonn
%O A056713 0,2
%A A056713 Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 11 2000
%E A056713 8687 from Hugo Pfoertner, Oct 19 2004

Form 533..333
%I A056714
%S A056714 0,1,3,13,25,49,143,419,1705
%N A056714 Numbers n such that 5*10^n + 3*R_n is prime, where R_n = 11...1 is the 
repunit (A002275) of length n.
%C A056714 Also numbers n such that (16*10^n-1)/3 is prime.
%C A056714 5*10^a(n)+3*(10^a(n)-1)/9 is a solution for part (b) of questions of 
puzzle 244 from www.primepuzzles.net. If a(n) is greater than 5812 then a(n) is an 
example that is asked for in this question. - Farideh Firoozbakht 
(f.firoozbakht(AT)sci.ui.ac.ir), Dec 02 2003
%H A056714 Prime Puzzles, <a 
href="http://www.primepuzzles.net/problems/prob_244.htm">Puzzle 244</a>
%H A056714 M. Kamada, <a 
href="http://homepage2.nifty.com/m_kamada/math/53333.htm">Factorizations of 
533...33</a>
%t A056714 Do[ If[ PrimeQ[ 5*10^n + 3*(10^n-1)/9], Print[n]], {n, 0, 5000}]
%K A056714 hard,nonn
%O A056714 0,3
%A A056714 Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 11 2000
%E A056714 1705 from Farideh Firoozbakht (f.firoozbakht(AT)sci.ui.ac.ir), Dec 18 2003

Form 577..777
%I A056715
%S A056715 0,2,8,14,17,18,33,35,126,183,324,344,866,992,1226,2355
%N A056715 Numbers n such that 5*10^n + 7*R_n is prime, where R_n = 11...1 is the 
repunit (A002275) of length n.
%C A056715 Also numbers n such that (52*10^n-7)/9 is prime.
%H A056715 M. Kamada, <a 
href="http://homepage2.nifty.com/m_kamada/math/57777.htm">Factorizations of 
577...77</a>
%t A056715 Do[ If[ PrimeQ[ 5*10^n + 7*(10^n-1)/9], Print[n]], {n, 0, 5000}]
%K A056715 hard,nonn
%O A056715 0,2
%A A056715 Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 11 2000

Form 599..999
%I A056716
%S A056716 0,1,2,4,5,7,10,13,22,23,28,34,40,61,73,361,490,613,1624,2000,2994,4301,
%T A056716 4332
%N A056716 Numbers n such that 6*10^n-1 is prime.
%C A056716 Also numbers n such that 5*10^n + 9*R_n is prime, where R_n = 11...1 is 
the repunit (A002275) of length n.
%C A056716 Next term is > 15000. - Hugo Pfoertner (hugo(AT)pfoertner.org), Feb 12 2004
%H A056716 M. Kamada, <a 
href="http://homepage2.nifty.com/m_kamada/math/59999.htm">Factorizations of 
599...99</a>
%t A056716 Do[ If[ PrimeQ[ 6*10^n - 1], Print[n]], {n, 0, 5000}]
%Y A056716 Cf. A056805 (6*10^n+1 is prime).
%K A056716 hard,nonn
%O A056716 0,3
%A A056716 Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 11 2000
%E A056716 More terms from Hugo Pfoertner (hugo(AT)pfoertner.org), Feb 12 2004
%E A056716 Other known primes: 18668, 32544, 34936.

Form 611..111
%I A056717
%S A056717 1,5,7,25,31,112,199,533,616,718,787,1357,2779,3889,4192,7537,7945
%N A056717 Numbers n such that 6*10^n + R_n is prime, where R_n = 11...1 is the 
repunit (A002275) of length n.
%C A056717 Also numbers n such that (55*10^n-1)/9 is prime.
%H A056717 M. Kamada, <a 
href="http://homepage2.nifty.com/m_kamada/math/61111.htm">Factorizations of 
611...11</a>
%t A056717 Do[ If[ PrimeQ[ 6*10^n + (10^n-1)/9], Print[n]], {n, 0, 10000}]
%K A056717 hard,nonn
%O A056717 0,2
%A A056717 Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 11 2000
%E A056717 2779,3889,4192,7537,7945 from Hugo Pfoertner (hugo(AT)pfoertner.org), 
Oct 19 2004

Form 677..777
%I A056718
%S A056718 1,2,4,10,13,25,115,179,181,238,785,799,1193,1730,1811,1871,2116,2180
%N A056718 6*10^n + 7*R_n, where R_n = 11...1 is the repunit (A002275) of length n.
%C A056718 Also numbers n such that (61*10^n-7)/9 is prime.
%H A056718 M. Kamada, <a 
href="http://homepage2.nifty.com/m_kamada/math/67777.htm">Factorizations of 
677...77</a>
%t A056718 Do[ If[ PrimeQ[ 6*10^n + 7*(10^n-1)/9], Print[n]], {n, 0, 5000}]
%K A056718 hard,nonn
%O A056718 0,2
%A A056718 Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 11 2000

Form 711..111
%I A056719
%S A056719 0,1,7,55
%N A056719 Numbers n such that 7*10^n + R_n is prime, where R_n = 11...1 is the 
repunit (A002275) of length n.
%C A056719 Also numbers n such that (64*10^n-1)/9 is prime.
%H A056719 M. Kamada, <a 
href="http://homepage2.nifty.com/m_kamada/math/71111.htm">Factorizations of 
711...11</a>
%t A056719 Do[ If[ PrimeQ[ 7*10^n + (10^n-1)/9], Print[n]], {n, 0, 35076}]
%K A056719 bref,hard,nonn
%O A056719 0,3
%A A056719 Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 11 2000

Form 733..333
%I A056720
%S A056720 0,1,2,3,5,53,56,343,908,1079,2204,2379
%N A056720 Numbers n such that 7*10^n + 3*R_n is prime, where R_n = 11...1 is the 
repunit (A002275) of length n.
%C A056720 Also numbers n such that (22*10^n-1)/3 is prime.
%H A056720 M. Kamada, <a 
href="http://homepage2.nifty.com/m_kamada/math/73333.htm">Factorizations of 
733...33</a>
%t A056720 Do[ If[ PrimeQ[ 7*10^n + 3*(10^n-1)/9], Print[n]], {n, 0, 5000}]
%K A056720 hard,nonn
%O A056720 0,3
%A A056720 Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 11 2000

Form 799..999
%I A056721
%S A056721 0,1,4,5,8,10,25,49,76,128,175,238,550,796,1219,2012,2846
%N A056721 Numbers n such that 8*10^n-1 is prime.
%C A056721 Also numbers n such that 7*10^n + 9*R_n is prime, where R_n = 11...1 is 
the repunit (A002275) of length n.
%H A056721 M. Kamada, <a 
href="http://homepage2.nifty.com/m_kamada/math/79999.htm">Factorizations of 
799...99</a>
%t A056721 Do[ If[ PrimeQ[ 7*10^n + (10^n-1)], Print[n]], {n, 0, 3000}]
%K A056721 hard,nonn
%O A056721 0,3
%A A056721 Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 11 2000
%E A056721 Other known primes: 11336, 49808.

Form 811..111
%I A056722
%S A056722 2,3,26,110,141,474,902,1746,2997,3627,3788
%N A056722 Numbers n such that 8*10^n + R_n is prime, where R_n = 11...1 is the 
repunit (A002275) of length n.
%C A056722 Also numbers n such that (73*10^n-1)/9 is prime.
%H A056722 M. Kamada, <a 
href="http://homepage2.nifty.com/m_kamada/math/81111.htm">Factorizations of 
811...11</a>
%t A056722 Do[ If[ PrimeQ[ 8*10^n + (10^n-1)/9], Print[n]], {n, 0, 5000}]
%K A056722 hard,nonn
%O A056722 0,1
%A A056722 Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 11 2000

Form 833..333
%I A056723
%S A056723 1,7,23,29,133,173,367,1925,3707,5765,9769
%N A056723 Numbers n such that 8*10^n + 3*R_n is prime, where R_n = 11...1 is the 
repunit (A002275) of length n.
%C A056723 Also numbers n such that (25*10^n-1)/3 is prime.
%H A056723 M. Kamada, <a 
href="http://homepage2.nifty.com/m_kamada/math/83333.htm">Factorizations of 
833...33</a>
%t A056723 Do[ If[ PrimeQ[ 8*10^n + 3*(10^n-1)/9], Print[n]], {n, 0, 10000}]
%K A056723 hard,nonn
%O A056723 0,2
%A A056723 Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 11 2000

Form 877..777
%I A056724
%S A056724 2,9,15,32,38,65,123,173,257,320,326,639,719,774,902
%N A056724 Numbers n such that 8*10^n + 7*R_n is prime, where R_n = 11...1 is the 
repunit (A002275) of length n.
%C A056724 Also numbers n such that (79*10^n-7)/9 is prime.
%H A056724 M. Kamada, <a 
href="http://homepage2.nifty.com/m_kamada/math/87777.htm">Factorizations of 
877...77</a>
%t A056724 Do[ If[ PrimeQ[ 8*10^n + 7*(10^n-1)/9], Print[n]], {n, 0, 10000}]
%K A056724 hard,nonn
%O A056724 0,1
%A A056724 Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 11 2000

Form 899..999
%I A056725
%S A056725 1,3,7,19,29,37,93,935
%N A056725 Numbers n such that 9*10^n - 1 is prime.
%C A056725 Also numbers n such that 8*10^n + 9*R_n is prime, where R_n = 11...1 is 
the repunit (A002275) of length n.
%H A056725 M. Kamada, <a 
href="http://homepage2.nifty.com/m_kamada/math/89999.htm">Factorizations of 
899...99</a>
%t A056725 Do[ If[ PrimeQ[ 8*10^n + (10^n-1)], Print[n]], {n, 1, 6750, 2}]
%Y A056725 Cf. A003307, A002235, A046865, A079906, A046866, A001771, A005541, 
A046867, A079907.
%K A056725 hard,nonn
%O A056725 0,2
%A A056725 Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 11 2000
%E A056725 There are no more terms up to 6750. - Robert G. Wilson v, Jan 26 2003
%E A056725 Other known primes: 8415, 9631, 11143, 41475, 41917, 48051, 107664.

Form 911..111
%I A056726
%S A056726 2,5,20,41,47,92,161,401,455
%N A056726 Numbers n such that 9*10^n + R_n is prime, where R_n = 11...1 is the 
repunit (A002275) of length n.
%C A056726 Also numbers n such that (82*10^n-1)/9 is prime.
%H A056726 M. Kamada, <a 
href="http://homepage2.nifty.com/m_kamada/math/91111.htm">Factorizations of 
911...11</a>
%t A056726 Do[ If[ PrimeQ[ 9*10^n + (10^n-1)/9], Print[n]], {n, 0, 5000}]
%K A056726 hard,nonn
%O A056726 0,1
%A A056726 Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 11 2000

Form 977..777
%I A056727
%S A056727 1,2,4,19,28,73,203,220,274,292,470,763,1891,3307,7007,7306,9755
%N A056727 Numbers n such that 9*10^n + 7*R_n is prime, where R_n = 11...1 is the 
repunit (A002275) of length n.
%C A056727 Also numbers n such that (88*10^n-7)/9 is prime.
%H A056727 M. Kamada, <a 
href="http://homepage2.nifty.com/m_kamada/math/97777.htm">Factorizations of 
977...77</a>
%t A056727 Do[ If[ PrimeQ[ 9*10^n + 7*(10^n-1)/9], Print[n]], {n, 0, 10000}]
%Y A056727 Cf. A093944 (corresponding primes).
%K A056727 hard,nonn
%O A056727 0,2
%A A056727 Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 11 2000