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

%I #22 Sep 03 2017 21:55:16

%S 13,37,223,1087,1423,1483,2683,4783,20743,27733,29017,33343,33613,

%T 35527,42457,44263,45817,55813,93487,108877,110917,113143,118897,

%U 151237,165703,187123,198823,203653,205417,221713,234187,234457,258607

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

%C Equivalently, p, p+4, p+6, p+10 and p+16 are consecutive primes.

%C Subsequence of A052378. - _R. J. Mathar_, Feb 11 2013

%C All terms = {7, 13} mod 30. - _Muniru A Asiru_, Aug 21 2017

%H R. J. Mathar, <a href="/A078952/b078952.txt">Table of n, a(n) for n = 1..1000</a>

%H R. J. Mathar, <a href="/A022004/a022004_1.pdf">Table of Prime Gap Constellations</a>

%e 37 is in the sequence since 37, 41, 43, 47 and 53 are consecutive primes.

%p 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 With[{s = Differences@ Prime@ Range[10^5]}, Prime[SequencePosition[s, {4, 2, 4, 6}][[All, 1]]]] (* _Michael De Vlieger_, Aug 21 2017 *)

%o (GAP)

%o K:=2*10^7+1;; # to get all terms <= K.

%o P:=Filtered([1,3..K],IsPrime);; I:=[4,2,4,6];;

%o P1:=List([1..Length(P)-1],i->P[i+1]-P[i]);;

%o P2:=List([1..Length(P)-Length(I)],i->[P1[i],P1[i+1],P1[i+2],P1[i+3]]);;

%o P3:=List(Positions(P2,I),i->P[i]); # _Muniru A Asiru_, Aug 21 2017

%o (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

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

%K nonn

%O 1,1

%A _Labos Elemer_, Dec 19 2002

%E Edited by _Dean Hickerson_, Dec 20 2002