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

13, 37, 223, 1087, 1423, 1483, 2683, 4783, 20743, 27733, 29017, 33343, 33613, 35527, 42457, 44263, 45817, 55813, 93487, 108877, 110917, 113143, 118897, 151237, 165703, 187123, 198823, 203653, 205417, 221713, 234187, 234457, 258607, 276817, 284227, 289837, 308923

Offset: 1

Author

Labos Elemer, Dec 19 2002

Keywords

• nonn

Comments

Equivalently, primes p such that p, p+4, p+6, p+10 and p+16 are consecutive primes.

All terms = {7, 13} mod 30. - Muniru A Asiru, Aug 21 2017

Examples

			37 is in the sequence since 37, 41 = 37 + 4, 43 = 37 + 6, 47 = 37 + 10 and 53 = 37 + 16 are consecutive primes.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from R. J. Mathar)
• R. J. Mathar, Table of Prime Gap Constellations.

Crossrefs

Subsequence of A052378. - R. J. Mathar, Feb 11 2013

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

Programs

GAP

K:=2*10^7+1;; # to get all terms <= K.
P:=Filtered([1,3..K],IsPrime);;  I:=[4,2,4,6];;
P1:=List([1..Length(P)-1],i->P[i+1]-P[i]);;
P2:=List([1..Length(P)-Length(I)],i->[P1[i],P1[i+1],P1[i+2],P1[i+3]]);;
P3:=List(Positions(P2,I),i->P[i]); # Muniru A Asiru, Aug 21 2017

Maple

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

Mathematica

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

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

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

Extensions

Edited by Dean Hickerson, Dec 20 2002