A078954 - OEIS

%I #19 Feb 21 2025 06:12:38

%S 1597,3907,12097,12907,38317,58897,65827,90007,90187,112237,129277,

%T 134077,140407,176317,204427,336757,374977,390097,394717,435637,

%U 486667,538147,543997,588937,618577,678637,702337,922627,990277,996157,1086247,1248337,1326037,1348537

%N Primes p such that the differences between the 5 consecutive primes starting with p are (4,6,2,4).

%C Equivalently, primes p such that p, p+4, p+10, p+12 and p+16 are consecutive primes.

%H Amiram Eldar, <a href="/A078954/b078954.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..500 from R. J. Mathar)

%F a(n) == 7 (mod 30). - _Amiram Eldar_, Feb 21 2025

%e 90007 is in the sequence since 90007, 90011 = 90007 + 4, 90017 = 90007 + 10, 90019 = 90007 + 12 and 90023 = 90007 + 16 are consecutive primes.

%t Transpose[Select[Partition[Prime[Range[85000]],5,1],Differences[#] == {4,6,2,4}&]][[1]] (* _Harvey P. Dale_, Sep 30 2012 *)

%o (PARI) list(lim) = {my(p1 = 2, p2 = 3, p3 = 5, p4 = 7); forprime(p5 = 11, lim, if(p2 - p1 == 4 && p3 - p2 == 6 && p4 - p3 == 2 && p5 - p4 == 4, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5);} \\ _Amiram Eldar_, Feb 21 2025

%Y Subsequence of A078851. - _R. J. Mathar_, Feb 11 2013

%Y Cf. A001223, A078866, A078867, A078946-A078971, A022006, A022007.

%K nonn,changed

%O 1,1

%A _Labos Elemer_, Dec 19 2002

%E Edited by _Dean Hickerson_, Dec 20 2002