

A100319


Even numbers m such that at least one of m1 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
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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).  JuriStepan Gerasimov, Nov 09 2009


LINKS

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


FORMULA

a(n) = A167692(n+1).  JuriStepan 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(n1)+isprime(n+1)<=1, print1(n, ", ")))
(Sage) [n for n in (3..250) if mod(n, 2)==0 and (is_prime(n1) + 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 n1 and n+1 is prime).
Cf. A167692(the even nonisolated nonprimes).  JuriStepan 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



