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A100319 Even numbers m such that at least one of m-1 and m+1 is composite. 3

%I

%S 8,10,14,16,20,22,24,26,28,32,34,36,38,40,44,46,48,50,52,54,56,58,62,

%T 64,66,68,70,74,76,78,80,82,84,86,88,90,92,94,96,98,100,104,106,110,

%U 112,114,116,118,120,122,124,126,128,130,132,134,136,140,142,144,146,148

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

%C 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).

%C The even nonisolated primes(n+1). - _Juri-Stepan Gerasimov_, Nov 09 2009

%H G. C. Greubel, <a href="/A100319/b100319.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = A167692(n+1). - _Juri-Stepan Gerasimov_, Nov 09 2009

%t Select[2*Range[100], CompositeQ[#-1] || CompositeQ[#+1] &] (* _G. C. Greubel_, Mar 09 2019 *)

%o (PARI) forstep(n=4,300,2,if(isprime(n-1)+isprime(n+1)<=1,print1(n,",")))

%o (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

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

%Y Cf. A167692(the even nonisolated nonprimes). - _Juri-Stepan Gerasimov_, Nov 09 2009

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

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

%K nonn

%O 1,1

%A _Rick L. Shepherd_, Nov 13 2004

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Last modified August 8 05:50 EDT 2020. Contains 336290 sequences. (Running on oeis4.)