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A078956 Primes p such that the differences between the 5 consecutive primes starting with p are (4,6,6,2).

%I A078956 #32 Feb 21 2025 06:22:32
%S A078956 43,163,643,1213,2953,4003,7573,11923,14533,25453,26683,26713,29863,
%T A078956 41593,48523,61543,68473,150193,151153,172423,206803,227593,290023,
%U A078956 302563,338563,343813,346543,428023,527053,529033,540373,547483,551713,570403,577513,622603,628993
%N A078956 Primes p such that the differences between the 5 consecutive primes starting with p are (4,6,6,2).
%C A078956 Equivalently, primes p such that p, p+4, p+10, p+16 and p+18 are consecutive primes.
%C A078956 All terms == 13 (mod 30). - _Robert Israel_, Oct 17 2023
%H A078956 Jon E. Schoenfield, <a href="/A078956/b078956.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Robert Israel)
%e A078956 43 is in the sequence since 43, 47 = 43 + 4, 53 = 43 + 10, 59 = 43 + 16 and 61 = 43 + 18 are consecutive primes.
%p A078956 L:= [0$5]:
%p A078956 p:= 1: R:= NULL: count:= 0:
%p A078956 while count < 100 do
%p A078956   p:= nextprime(p);
%p A078956   L:= [L[2],L[3],L[4],L[5],p];
%p A078956   if L -~ L[1] = [0, 4, 10, 16, 18] then
%p A078956     count:= count+1;
%p A078956     R:= R, L[1];
%p A078956   fi
%p A078956 od:
%p A078956 R; # _Robert Israel_, Oct 17 2023
%t A078956 Select[Partition[Prime[Range[50000]],5,1],Differences[#]=={4,6,6,2}&][[All,1]] (* _Harvey P. Dale_, Jan 23 2021 *)
%o A078956 (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 == 6 && p5 - p4 == 2, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5);} \\ _Amiram Eldar_, Feb 21 2025
%Y A078956 Subsequence of A078852. - _R. J. Mathar_, May 06 2017
%Y A078956 Cf. A001223, A078866, A078867, A078946-A078969, A022006, A022007.
%K A078956 nonn
%O A078956 1,1
%A A078956 _Labos Elemer_, Dec 19 2002
%E A078956 Edited by _Dean Hickerson_, Dec 20 2002