# [seqfan] Re: A080906?

RGWv rgwv at rgwv.com
Sun Dec 7 20:24:54 CET 2008

```et al,

Here is what I get, and I disagree with the figure that Robert
Israel have for the number of terms of length 6; he has 3223 and I get 2741.

Sequentially yours,

Robert G. Wilson, v

%I A080906
%S A080906
23,37,53,73,1103,1117,1123,1129,1153,1171,1303,1307,1319,1361,1367,1373,
%T A080906
1723,1741,1747,1753,1759,1783,1789,1907,1913,1931,1973,1979,1997,2311,
%U A080906
2341,2347,2371,2383,2389,2903,2917,2953,2971,3119,3137,3167,3719,3761
%N A080906 Prime numbers with 2k digits such that the first k-digit
number and the last (second) k-digit number are both prime numbers with
padding of zeroes allowed in second k-digit number.
%C A080906 The number of terms of 2k digits: 4, 92, 2741, 103247, ..., .
- Robert G. Wilson v, Dec 07 2008.
%F A080906 P. Giannopoulos, The brainteasers (unpublished).
%H A080906 Robert G. Wilson v, Table of n, for n = 1..1000.
<http://www.research.att.com/%7Enjas/sequences/b080906.txt>.
%t A080906 f[n_] := Block[{c = 0, lp = PrimePi[10^n] - PrimePi[10^(n -
1)], lq = PrimePi[10^n], lst = {}, pq, p = Prime@ Range[PrimePi[10^(n -
1)] + 1, PrimePi[10^n]], q = Prime@ Range[1, PrimePi[10^n]]}, Do[ pq =
p[[i]]*10^(2 n - 2) + q[[j]]; If[ PrimeQ@ pq, AppendTo[lst, pq]; c++],
{i, lp}, {j, lq}]; lst] - Robert G. Wilson v, Dec 07 2008.
%Y A080906 Cf. A000040.
%K A080906 base,easy,nonn
%O A080906 1,1
%A A080906 P. Giannopoulos (pgiannop1(AT)yahoo.com), Mar 31 2003
%E A080906 Corrected, edited and extended by Zak Seidov
(zakseidov at yahoo.com), Robert Israel (israel at math.ubc.ca), Farideh
Firoozbakht (f.firoozbakht at sci.ui.ac.ir) and Robert G. Wilson v
(rgwv at rgwv.com), Dec 07 2008.

The b-text file is:

23, 37, 53, 73, 1103, 1117, 1123, 1129, 1153, 1171, 1303, 1307, 1319,
1361, 1367, 1373, 1723, 1741, 1747, 1753, 1759, 1783, 1789, 1907, 1913,
1931, 1973, 1979, 1997, 2311, 2341, 2347, 2371, 2383, 2389, 2903, 2917,
2953, 2971, 3119, 3137, 3167, 3719, 3761, 3767, 3779, 3797, 4111, 4129,
4153, 4159, 4337, 4373, 4397, 4703, 4723, 4729, 4759, 4783, 4789, 5303,
5323, 5347, 5903, 5923, 5953, 6113, 6131, 6143, 6173, 6197, 6703, 6719,
6737, 6761, 6779, 7103, 7129, 7159, 7307, 7331, 7907, 7919, 7937, 8311,
8317, 8329, 8353, 8389, 8923, 8929, 8941, 8971, 9719, 9743, 9767,
1010003, 1010083, 1010131, 1010167, 1010179, 1010263, 1010353, 1010419,
1010431, 1010461, 1010467, 1010491, 1010509, 1010617, 1010683, 1010719,
1010797, 1010809, 1010881, 1010929, 1010983, 1030019, 1030031, 1030061,
1030067, 1030157, 1030181, 1030241, 1030307, 1030349, 1030439, 1030571,
1030619, 1030643, 1030739, 1030751, 1030787, 1030811, 1030823, 1030919,
1070011, 1070131, 1070149, 1070197, 1070233, 1070257, 1070317, 1070347,
1070389, 1070431, 1070491, 1070557, 1070569, 1070659, 1070683, 1070761,
1070827, 1070947, 1090003, 1090013, 1090031, 1090097, 1090127, 1090151,
1090181, 1090211, 1090241, 1090373, 1090409, 1090421, 1090457, 1090577,
1090613, 1090709, 1090757, 1090769, 1090877, 1090883, 1090919, 1090937,
1090967, 1090997, 1130011, 1130023, 1130047, 1130053, 1130131, 1130191,
1130251, 1130257, 1130281, 1130293, 1130317, 1130359, 1130431, 1130587,
1130641, 1130677, 1130719, 1130809, 1130827, 1130863, 1130929, 1130947,
1130953, 1270013, 1270067, 1270079, 1270097, 1270103, 1270151, 1270193,
1270271, 1270337, 1270421, 1270433, 1270499, 1270541, 1270547, 1270571,
1270757, 1270823, 1270859, 1310041, 1310053, 1310083, 1310137, 1310233,
1310251, 1310269, 1310293, 1310311, 1310359, 1310383, 1310389, 1310431,
1310467, 1310509, 1310599, 1310719, 1310797, 1310809, 1370053, 1370059,
1370101, 1370113, 1370197, 1370227, 1370263, 1370269, 1370311, 1370359,
1370389, 1370431, 1370449, 1370461, 1370491, 1370503, 1370521, 1370587,
1370599, 1370617, 1370683, 1370701, 1370773, 1370821, 1370839, 1370857,
1370953, 1370977, 1390003, 1390019, 1390043, 1390157, 1390199, 1390241,
1390283, 1390331, 1390409, 1390421, 1390457, 1390541, 1390547, 1390601,
1390607, 1390619, 1390643, 1390709, 1390733, 1390757, 1390859, 1390919,
1390937, 1390967, 1490011, 1490029, 1490059, 1490089, 1490179, 1490233,
1490257, 1490317, 1490347, 1490353, 1490443, 1490479, 1490557, 1490641,
1490647, 1490677, 1490701, 1490743, 1490773, 1490941, 1490953, 1510013,
1510043, 1510109, 1510163, 1510199, 1510307, 1510337, 1510373, 1510541,
1510601, 1510643, 1510757, 1510853, 1510877, 1510967, 1510991, 1570007,
1570043, 1570061, 1570067, 1570073, 1570097, 1570193, 1570199, 1570229,
1570241, 1570271, 1570421, 1570433, 1570487, 1570577, 1570607, 1570619,
1570631, 1570769, 1570859, 1570883, 1570937, 1570967, 1570991, 1630019,
1630127, 1630193, 1630199, 1630367, 1630379, 1630457, 1630463, 1630547,
1630619, 1630829, 1630859, 1630919, 1670003, 1670017, 1670059, 1670089,
1670269, 1670281, 1670353, 1670359, 1670419, 1670491, 1670503, 1670563,
1670569, 1670653, 1670659, 1670761, 1670827, 1670857, 1670863, 1670887,
1670953, 1670971, 1670983, 1730041, 1730089, 1730101, 1730149, 1730167,
1730263, 1730317, 1730353, 1730431, 1730461, 1730683, 1730797, 1730809,
1730863, 1730887, 1730929, 1730941, 1730983, 1790029, 1790053, 1790059,
1790071, 1790137, 1790149, 1790233, 1790263, 1790293, 1790311, 1790353,
1790359, 1790401, 1790419, 1790443, 1790479, 1790521, 1790557, 1790587,
1790599, 1790641, 1790647, 1790683, 1790743, 1790809, 1790857, 1790863,
1810013, 1810043, 1810097, 1810199, 1810241, 1810271, 1810283, 1810337,
1810397, 1810409, 1810421, 1810433, 1810439, 1810577, 1810607, 1810709,
1810733, 1810751, 1810877, 1810937, 1810967, 1910023, 1910047, 1910059,
1910071, 1910101, 1910107, 1910131, 1910179, 1910257, 1910263, 1910269,
1910401, 1910509, 1910593, 1910677, 1910683, 1910719, 1910827, 1910911,
1910941, 1910971, 1910977, 1930043, 1930073, 1930079, 1930139, 1930199,
1930307, 1930349, 1930373, 1930433, 1930541, 1930757, 1930811, 1930823,
1930883, 1930937, 1970029, 1970071, 1970083, 1970149, 1970233, 1970257,
1970263, 1970359, 1970401, 1970431, 1970461, 1970467, 1970491, 1970599,
1970641, 1970677, 1970719, 1970743, 1970809, 1970977, 1990007, 1990031,
1990103, 1990151, 1990211, 1990223, 1990229, 1990277, 1990337, 1990379,
1990433, 1990463, 1990487, 1990523, 1990577, 1990607, 1990643, 1990661,
1990691, 1990787, 1990823, 1990829, 1990883, 1990907, 2110019, 2110037,
2110103, 2110151, 2110223, 2110313, 2110337, 2110439, 2110523, 2110547,
2110673, 2110709, 2110751, 2110769, 2110811, 2110853, 2110859, 2110877,
2230061, 2230079, 2230097, 2230139, 2230157, 2230331, 2230409, 2230433,
2230439, 2230457, 2230541, 2230577, 2230643, 2230673, 2230691, 2230727,
2230829, 2270003, 2270011, 2270071, 2270113, 2270131, 2270137, 2270173,
2270179, 2270239, 2270251, 2270263, 2270269, 2270311, 2270383, 2270449,
2270599, 2270641, 2270659, 2270677, 2270683, 2270773, 2270839, 2270929,
2270941, 2270953, 2270977, 2290003, 2290007, 2290031, 2290037, 2290097,
2290139, 2290151, 2290181, 2290283, 2290499, 2290523, 2290571, 2290619,
2290643, 2290727, 2290751, 2290829, 2290907, 2290991, 2330047, 2330101,
2330191, 2330197, 2330227, 2330281, 2330389, 2330431, 2330491, 2330617,
2330641, 2330719, 2330761, 2330827, 2330929, 2330941, 2330947, 2330953,
2390023, 2390053, 2390071, 2390191, 2390197, 2390263, 2390389, 2390431,
2390449, 2390617, 2390653, 2390743, 2390797, 2390809, 2390887, 2390911,
2410043, 2410127, 2410181, 2410271, 2410313, 2410337, 2410367, 2410433,
2410523, 2410571, 2410601, 2410613, 2410631, 2410643, 2410829, 2410907,
2410937, 2410997, 2510017, 2510023, 2510041, 2510047, 2510083, 2510107,
2510149, 2510227, 2510293, 2510401, 2510449, 2510491, 2510503, 2510653,
2510701, 2510743, 2510941, 2510947, 2510971, 2570011, 2570017, 2570047,
2570083, 2570137, 2570233, 2570251, 2570311, 2570317, 2570389, 2570401,
2570419, 2570431, 2570467, 2570509, 2570563, 2570599, 2570677, 2570683,
2570761, 2570773, 2570809, 2570941, 2630041, 2630107, 2630179, 2630197,
2630239, 2630281, 2630317, 2630389, 2630431, 2630491, 2630521, 2630557,
2630587, 2630599, 2630743, 2630773, 2630839, 2630857, 2630863, 2690003,
2690041, 2690047, 2690053, 2690059, 2690071, 2690089, 2690137, 2690167,
2690173, 2690179, 2690197, 2690239, 2690263, 2690293, 2690353, 2690383,
2690431, 2690491, 2690557, 2690587, 2690593, 2690599, 2690659, 2690719,
2690773, 2690827, 2690887, 2690911, 2710003, 2710007, 2710013, 2710151,
2710193, 2710241, 2710313, 2710373, 2710397, 2710439, 2710457, 2710541,
2710571, 2710823, 2710907, 2710937, 2710997, 2770043, 2770199, 2770211,
2770241, 2770367, 2770499, 2770571, 2770577, 2770613, 2770673, 2770769,
2770829, 2770883, 2770907, 2770991, 2810011, 2810029, 2810089, 2810107,
2810167, 2810173, 2810191, 2810257, 2810317, 2810359, 2810503, 2810617,
2810641, 2810653, 2810683, 2810827, 2810881, 2810911, 2830067, 2830073,
2830097, 2830151, 2830181, 2830229, 2830277, 2830349, 2830367, 2830379,
2830397, 2830433, 2830439, 2830523, 2830547, 2830577, 2830613, 2830631,
2830787, 2830853, 2830859, 2830937, 2830967, 2930003, 2930071, 2930113,
2930167, 2930173, 2930197, 2930281, 2930359, 2930401, 2930419, 2930449,
2930491, 2930509, 2930563, 2930593, 2930743, 2930761, 2930773, 2930839,
2930887, 2930911, 2930947, 3070003, 3070031, 3070037, 3070043, 3070061,
3070073, 3070079, 3070127, 3070139, 3070337, 3070349, 3070373, 3070499,
3070541, 3070547, 3070601, 3070619, 3070709, 3070787, 3070853, 3070877,
3070883, 3070997, 3110011, 3110059, 3110101, 3110179, 3110227, 3110251,
3110293, 3110353, 3110431, 3110563, 3110593, 3110617, 3110647, 3110683,
3110761, 3110797, 3110929, 3110953, 3130007, 3130019, 3130031, 3130037,
3130097, 3130199, 3130229, 3130241, 3130331, 3130367, 3130373, 3130409,
3130487, 3130541, 3130571, 3130577, 3130619, 3130733, 3130739, 3130823,
3130997, 3170053, 3170059, 3170107, 3170137, 3170149, 3170179, 3170227,
3170263, 3170281, 3170311, 3170383, 3170467, 3170521, 3170617, 3170659,
3170743, 3170887, 3170911, 3170953, 3170983, 3310061, 3310079, 3310127,
3310193, 3310271, 3310283, 3310457, 3310547, 3310577, 3310691, 3310739,
3310757, 3310829, 3310859, 3310877, 3370013, 3370043, 3370109, 3370127,
3370151, 3370181, 3370313, 3370331, 3370421, 3370457, 3370541, 3370571,
3370691, 3370739, 3370751, 3370769, 3370823, 3370877, 3370883, 3370907,
3370919, 3370937, 3370967, 3470003, 3470011, 3470017, 3470029, 3470083,
3470101, 3470113, 3470167, 3470191, 3470239, 3470251, 3470353, 3470443,
3470491, 3470587, 3470617, 3470647, 3470653, 3470683, 3470743, 3470821,
3470827, 3470881, 3470947, 3470983, 3490031, 3490127, 3490139, 3490199

f.firoozbakht at sci.ui.ac.ir wrote:

>Dear Zak,
>
>You are right,
>
>1. 23 is missed.
>2. Terms after 1373 are wrong.
>3. Terms less than 4000 are:
>
>23, 37, 53, 73, 1103, 1117, 1123, 1129, 1153, 1171, 1303, 1307, 1319, 1361,
>1367, 1373, 1723, 1741, 1747, 1753, 1759, 1783, 1789, 1907, 1913, 1931, 1973,
>1979, 1997, 2311, 2341, 2347, 2371, 2383, 2389, 2903, 2917, 2953, 2971, 3119,
>3137, 3167, 3719, 3761, 3767, 3779, 3797
>
>4. I think the definition must change in this way:
>Prime numbers with 2k digits such that the first k-digit number and the last
>(second) k-digit number are both prime numbers.
>
>Farideh
>
>Quoting zak seidov <zakseidov at yahoo.com>:
>
>
>
>>Dear SeqFans,
>>
>>anyone may wish to edit this:
>>
>>1. 23 is missed
>>2. terms after 1373 are wrong
>>4. in %N, it'd be Prime numbers?
>>   otherwise why 22 32 52 72 missed?
>>
>>thx, zak
>>
>>PS Were i editor i'd returm it to author(?)
>>
>>%I A080906
>>%S A080906
>>37,53,73,1103,1117,1123,1129,1153,1171,1303,1307,1319,1361,1367,1373,
>>%T A080906 1523,1531,1543,1553,1559,1567,1571,1579,1583,1597
>>%N A080906 Numbers with 2k digits such that the first k digits and
>>the last k digits
>>               are both prime numbers.
>>%F A080906 P. Giannopoulos, The brainteasers (unpublished)
>>%Y A080906 Sequence in context: A092105 A101938 A060330
>>this_sequence A101940 A036540
>>               A141166
>>%Y A080906 Adjacent sequences: A080903 A080904 A080905 this_sequence
>> A080907 A080908
>>               A080909
>>%K A080906 base,easy,nonn
>>%O A080906 0,1
>>%A A080906 P. Giannopoulos (pgiannop1(AT)yahoo.com), Mar 31 2003
>>
>>
>>
>>
>>
>>_______________________________________________
>>
>>Seqfan Mailing list - http://list.seqfan.eu/
>>
>>
>>
>
>
>
>
>
>
>
>
>
>----------------------------------------------------------------
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>
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>
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>
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>

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