A271211 Composite integers sandwiched between primes p, q with q-p = 4.

8, 9, 10, 14, 15, 16, 20, 21, 22, 38, 39, 40, 44, 45, 46, 68, 69, 70, 80, 81, 82, 98, 99, 100, 104, 105, 106, 110, 111, 112, 128, 129, 130, 164, 165, 166, 194, 195, 196, 224, 225, 226, 230, 231, 232, 278, 279, 280, 308, 309, 310, 314, 315, 316, 350, 351, 352, 380

Offset: 1

Author

Michel Marcus, Apr 02 2016

Keywords

• nonn

Examples

			The composite number 8 is sandwiched between primes 7 and 11, and 11-7=4, so 8 is a member of the sequence.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Laurent Coppey, Décompositions multiplicatives directes des entiers, Diagrammes, 65-66 (2011), p. 1-68, in French, see J4 p. 11.

Crossrefs

Cf. A014574, A029710, A045881.

Programs

Mathematica

Range[#[[1]]+1,#[[2]]-1]&/@Select[Partition[Prime[Range[100]],2,1],#[[2]]- #[[1]] == 4&]//Flatten (* Harvey P. Dale, Oct 12 2019 *)

PARI

lista(nn) = {forcomposite(c=4, nn, if ((p=precprime(c)) && ((nextprime(c)-p)==4), print1(c, ", ")););}