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A217603 Consider sets of 3 consecutive primes a, b, c such that c - a = 100, then sequence gives the values of b.

%I A217603 #16 Jul 22 2024 18:05:10
%S A217603 58831,286927,360653,404941,590489,623107,651587,673747,710119,740801,
%T A217603 779413,794831,795427,1040311,1107269,1185241,1206869,1320437,1392007,
%U A217603 1568771,1581829,1599803,1601953,1613201,1721081,1744927,1942273,1951321,1994299,2024063
%N A217603 Consider sets of 3 consecutive primes a, b, c such that c - a = 100, then sequence gives the values of b.
%H A217603 Zak Seidov, <a href="/A217603/a217603.txt">Table of n, a, b, c for n=1..1000</a>
%H A217603 Zak Seidov, <a href="/A217603/a217603_1.txt">Table of n, a, b, c for n=1..1000</a>
%e A217603 a(1) = 58831 because {58789, 58831, 58889} is the first set of 3 consecutive primes a, b, c with c-a=100.
%e A217603 a(2) = 286927 because {286873, 286927, 286973} is the second set of 3 consecutive primes a, b, c with c-a=100.
%e A217603 a(1000) = 23090087 because {23090059, 23090087, 23090159} is the 1000th set of 3 consecutive primes a, b, c with c-a=100.
%t A217603 s = {}; a = 2; b = 3; c = 5; Do[If[c - a == 100, AppendTo[s, b]; Print[{a, b, c}]]; a = b; b = c; c = NextPrime[c], {10^5}]; s
%t A217603 Select[Partition[Prime[Range[151000]],3,1],#[[3]]-#[[1]]==100&][[;;,2]] (* _Harvey P. Dale_, Jul 22 2024 *)
%o A217603 (PARI) p=2;q=3;forprime(r=5,1e6,if(r-p==100,print1(q", "));p=q;q=r) \\ _Charles R Greathouse IV_, Nov 14 2012
%Y A217603 Cf. A166251, A217561, A217566, A217577.
%K A217603 nonn
%O A217603 1,1
%A A217603 _Zak Seidov_, Oct 08 2012