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A078963 Primes p such that the differences between the 5 consecutive primes starting with p are (6,4,6,2).

%I A078963 #26 Feb 22 2025 03:39:06
%S A078963 3313,4993,5851,9613,17971,23011,32353,36913,45121,51421,53881,54403,
%T A078963 59611,76243,90001,91951,127591,130633,131431,134353,140401,142963,
%U A078963 174061,229753,246913,267661,303361,311551,321313,340111,386143,435553,465061,514513,532993,618571
%N A078963 Primes p such that the differences between the 5 consecutive primes starting with p are (6,4,6,2).
%C A078963 Equivalently, primes p such that p, p+6, p+10, p+16 and p+18 are consecutive primes.
%H A078963 Amiram Eldar, <a href="/A078963/b078963.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Robert Israel)
%F A078963 From _Amiram Eldar_, Feb 22 2025: (Start)
%F A078963 a(n) == 1 (mod 6).
%F A078963 a(n) == 1 or 13 (mod 30). (End)
%e A078963 23011 is in the sequence since 23011, 23017 = 23011 + 6, 23021 = 23011 + 10, 23027 = 23011 + 16 and 23029 = 23011 + 18 are consecutive primes.
%p A078963 L:= [2,3,5,7,11]:
%p A078963 count:= 0: Res:= NULL:
%p A078963 while count < 50 do
%p A078963   L:= [op(L[2..5]),nextprime(L[5])];
%p A078963   if L - [L[1]$5] = [0,6,10,16,18] then
%p A078963     count:= count+1;
%p A078963     Res:= Res, L[1];
%p A078963   fi
%p A078963 od:
%p A078963 Res; # _Robert Israel_, Jun 04 2018
%t A078963 Transpose[Select[Partition[Prime[Range[50000]],5,1],Differences[#]=={6,4,6,2}&]][[1]]  (* _Harvey P. Dale_, Mar 04 2011 *)
%o A078963 (PARI) list(lim) = {my(p1 = 2, p2 = 3, p3 = 5, p4 = 7); forprime(p5 = 11, lim, if(p2 - p1 == 6 && p3 - p2 == 4 && p4 - p3 == 6 && p5 - p4 == 2, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5);} \\ _Amiram Eldar_, Feb 22 2025
%Y A078963 Subsequence of A078856. - _R. J. Mathar_, May 06 2017
%Y A078963 Cf. A001223, A078866, A078867, A078946-A078971, A022006, A022007.
%K A078963 nonn
%O A078963 1,1
%A A078963 _Labos Elemer_, Dec 19 2002
%E A078963 Edited by _Dean Hickerson_, Dec 20 2002