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A100319
Even numbers m such that at least one of m-1 and m+1 is composite.
3
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
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
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
KEYWORD
nonn
AUTHOR
Rick L. Shepherd, Nov 13 2004
STATUS
approved