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

1,1

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

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.

Example

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

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 *)

Prog

(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
(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

Crossrefs

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

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

Sequence in context: A155277 A090042 A266882 * A206279 A130621 A309594

Adjacent sequences: A078949 A078950 A078951 * A078953 A078954 A078955

Keyword

nonn

Author

Labos Elemer, Dec 19 2002

Extensions

Edited by Dean Hickerson, Dec 20 2002

Status

approved