# A076150

Ralf Stephan ralf at ark.in-berlin.de
Fri Nov 1 14:50:26 CET 2002

```  Bonjour!

Regarding...

%I A076150
%S A076150 201,321,511,531,621,841,891,1071,1131,1261,1331,1411,1461
%N A076150 m such that the decade m through m+9 is devoid of primes.
%C A076150 Since a decade of consecutive numbers may contain up to 4 primes,mor
e precisely a prime quadruplet(p,p+2,p+6,p+8) within a decade k through k+9,whe
re k=p-1 or p(=A007530)excepting the first case (2,3,5,7),this sequence may be
regarded as a counterpart to A007530.
%e A076150 531 is in the sequence because it is the first term of the ten conse
cutive composites:531=3^2*59;532=2^2*7*19;533=13*41;534=2*3*89;535=5*107;536=2^
3*67;537=3*179;538=2*269;539=7^2*11;540=2^2*3^3*5.
%Y A076150 Cf. A007530.
%K A076150 more,nonn,new
%O A076150 1,1
%A A076150 Lekraj Beedassy (beedassylekraj at hotmail.com), Oct 31 2002

... the entry is either nonsense or mistaken. If the submitter had meant
"start of ten consecutive composites" the sequence should have been

115, 117, 201, 213, 295, 297, 319, 321, 469, 511, 525, 527, 529, 531,
621, 663, 775, 777, 799, 841, 843, 865, 867, 889, 891, 893, 895, 897,
955, 957, 999, 1071, 1073, 1075, 1077, 1131, 1133, 1135, 1137, 1139,
1141,

but then the description is, um, a bit twisted. OTOH, if he meant "start of ten
consecutive composites, starting with n = 1 mod 10" then he missed eg 1141.
I'm willing to resubmit IFF there is interest.

Greets,
ralf

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