A100319 Even numbers m such that at least one of m-1 and m+1 is composite.

8, 10, 14, 16, 20, 22, 24, 26, 28, 32, 34, 36, 38, 40, 44, 46, 48, 50, 52, 54, 56, 58, 62, 64, 66, 68, 70, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 104, 106, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 140, 142, 144, 146, 148

Offset

1,1

Comments

Subsequence of A100318. For each k >= 0, a(k+1) = a(k) + 2 unless a(k) + 1 and a(k) + 3 are twin primes, in which case a(k+1) = a(k) + 4 (as a(k) - 1 and a(k) + 5 are divisible by 3).

The even nonisolated primes(n+1). - Juri-Stepan Gerasimov, Nov 09 2009

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Formula

a(n) = A167692(n+1). - Juri-Stepan Gerasimov, Nov 09 2009

Mathematica

Select[2*Range[100], CompositeQ[#-1] || CompositeQ[#+1] &]  (* G. C. Greubel, Mar 09 2019 *)

Prog

(PARI) forstep(n=4, 300, 2, if(isprime(n-1)+isprime(n+1)<=1, print1(n, ", ")))
(Sage) [n for n in (3..250) if mod(n, 2)==0 and (is_prime(n-1) + is_prime(n+1)) < 2] # G. C. Greubel, Mar 09 2019

Crossrefs

Cf. A100318 (supersequence containing odd and even n), A045718 (n such that at least one of n-1 and n+1 is prime).

Cf. A167692(the even nonisolated nonprimes). - Juri-Stepan Gerasimov, Nov 09 2009

Cf. A005818, A038179, A007310, A038511, A025584.

Complement of A014574 (average of twin prime pairs) w.r.t. A005843 (even numbers), except for missing term 2.

Sequence in context: A308874 A030490 A076639 * A167692 A171689 A163628

Adjacent sequences: A100316 A100317 A100318 * A100320 A100321 A100322

Keyword

nonn

Author

Rick L. Shepherd, Nov 13 2004

Status

approved