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A078948 Primes p such that the differences between the 5 consecutive primes starting with p are (2,6,4,2).

%I A078948 #28 Feb 21 2025 06:16:33
%S A078948 29,59,269,1289,2129,2789,5639,8999,13679,14549,18119,36779,62129,
%T A078948 75989,80669,83219,88799,93479,113159,115769,124769,132749,150209,
%U A078948 160079,163979,203309,207509,223829,228509,278489,282089,284729,298679,312929,313979,323369,337859
%N A078948 Primes p such that the differences between the 5 consecutive primes starting with p are (2,6,4,2).
%C A078948 Equivalently, primes p such that p, p+2, p+8, p+12 and p+14 are consecutive primes.
%C A078948 All terms are congruent to 29 (mod 30). - _Muniru A Asiru_, Sep 04 2017
%H A078948 Amiram Eldar, <a href="/A078948/b078948.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from R. J. Mathar)
%H A078948 R. J. Mathar, <a href="/A022004/a022004_1.pdf">Table of Prime Gap Constellations</a>.
%e A078948 59 is in the sequence since 59, 61 = 59 + 2, 67 = 59 + 8, 71 = 59 + 12 and 73 = 59 + 14 are consecutive primes.
%p A078948 for i from 1 to 10^5 do if [ithprime(i+1),ithprime(i+2),ithprime(i+3),ithprime(i+4)] = [ithprime(i)+2,ithprime(i)+8,ithprime(i)+12,ithprime(i)+14] then print(ithprime(i)); fi; od;  # _Muniru A Asiru_, Sep 04 2017
%t A078948 Select[Partition[Prime[Range[26000]],5,1],Differences[#]=={2,6,4,2}&][[;;,1]] (* _Harvey P. Dale_, Dec 10 2024 *)
%o A078948 (GAP)
%o A078948 K:=26*10^7+1;; # to get all terms <= K.
%o A078948 P:=Filtered([1,3..K],IsPrime);;  I:=[2,6,4,2];;
%o A078948 P1:=List([1..Length(P)-1],i->P[i+1]-P[i]);;
%o A078948 Q:=List(Positions(List([1..Length(P)-Length(I)],i->[P1[i],P1[i+1],P1[i+2],P1[i+3]]),I),i->P[i]); # _Muniru A Asiru_, Sep 04 2017
%o A078948 (PARI) list(lim) = {my(p1 = 2, p2 = 3, p3 = 5, p4 = 7); forprime(p5 = 11, lim, if(p2 - p1 == 2 && p3 - p2 == 6 && p4 - p3 == 4 && p5 - p4 == 2, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5);} \\ _Amiram Eldar_, Feb 21 2025
%Y A078948 Subsequence of A078848. - _R. J. Mathar_, Feb 10 2013
%Y A078948 Cf. A001223, A078866, A078867, A078946-A078971, A022006, A022007.
%K A078948 nonn
%O A078948 1,1
%A A078948 _Labos Elemer_, Dec 19 2002
%E A078948 Edited by _Dean Hickerson_, Dec 20 2002