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A078952 Primes p such that the differences between the 5 consecutive primes starting with p are (4,2,4,6).

%I A078952 #30 Feb 21 2025 06:18:56
%S A078952 13,37,223,1087,1423,1483,2683,4783,20743,27733,29017,33343,33613,
%T A078952 35527,42457,44263,45817,55813,93487,108877,110917,113143,118897,
%U A078952 151237,165703,187123,198823,203653,205417,221713,234187,234457,258607,276817,284227,289837,308923
%N A078952 Primes p such that the differences between the 5 consecutive primes starting with p are (4,2,4,6).
%C A078952 Equivalently, primes p such that p, p+4, p+6, p+10 and p+16 are consecutive primes.
%C A078952 All terms = {7, 13} mod 30. - _Muniru A Asiru_, Aug 21 2017
%H A078952 Amiram Eldar, <a href="/A078952/b078952.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from R. J. Mathar)
%H A078952 R. J. Mathar, <a href="/A022004/a022004_1.pdf">Table of Prime Gap Constellations</a>.
%e A078952 37 is in the sequence since 37, 41 = 37 + 4, 43 = 37 + 6, 47 = 37 + 10 and 53 = 37 + 16 are consecutive primes.
%p A078952 for i from 1 to 10^7 do if ithprime(i+1)=ithprime(i)+4 and ithprime(i+2)=ithprime(i)+6 and ithprime(i+3)=ithprime(i)+10 and ithprime(i+4)=ithprime(i)+16 then print(ithprime(i)); fi; od; # _Muniru A Asiru_, Aug 21 2017
%t A078952 With[{s = Differences@ Prime@ Range[10^5]}, Prime[SequencePosition[s, {4, 2, 4, 6}][[All, 1]]]] (* _Michael De Vlieger_, Aug 21 2017 *)
%o A078952 (GAP)
%o A078952 K:=2*10^7+1;; # to get all terms <= K.
%o A078952 P:=Filtered([1,3..K],IsPrime);;  I:=[4,2,4,6];;
%o A078952 P1:=List([1..Length(P)-1],i->P[i+1]-P[i]);;
%o A078952 P2:=List([1..Length(P)-Length(I)],i->[P1[i],P1[i+1],P1[i+2],P1[i+3]]);;
%o A078952 P3:=List(Positions(P2,I),i->P[i]); # _Muniru A Asiru_, Aug 21 2017
%o A078952 (PARI) lista(nn) = forprime(p=3, nn, if(nextprime(p+1)==p+4 && nextprime(p+5)==p+6 && nextprime(p+7)==p+10 && nextprime(p+11)==p+16, print1(p, ", "))); \\ _Altug Alkan_, Aug 21 2017
%o A078952 (PARI) list(lim) = {my(p1 = 2, p2 = 3, p3 = 5, p4 = 7); forprime(p5 = 11, lim, if(p2 - p1 == 4 && p3 - p2 == 2 && p4 - p3 == 4 && p5 - p4 == 6, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5);} \\ _Amiram Eldar_, Feb 21 2025
%Y A078952 Subsequence of A052378. - _R. J. Mathar_, Feb 11 2013
%Y A078952 Cf. A001223, A022006, A022007, A078866, A078867, A078946-A078971.
%K A078952 nonn
%O A078952 1,1
%A A078952 _Labos Elemer_, Dec 19 2002
%E A078952 Edited by _Dean Hickerson_, Dec 20 2002