A167692 -id:A167692 - cp's OEIS frontend

A168044 Half of the even nonisolated nonprimes A167692.

0, 4, 5, 7, 8, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 76, 77, 78, 79, 80, 81, 82, 83

Offset: 1

Juri-Stepan Gerasimov, Nov 17 2009

Apart from the first term, numbers n with at least one of 2n-1 and 2n+1 composite. - Charles R Greathouse IV, Mar 25 2010

It is possible to create a sieve for twin primes because these numbers are of the form i+j+2*i*j and 1+i+j+2*i*j for i,j >= 1. Except 1, complement of A040040 where 2*a(n)-1 and 2*a(n)+1 are twin primes. - Davide Rotondo, Jan 19 2021

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

Cf. A167692.

Except 1, complement of A040040.

Select[Range[0,100], Mod[#, 2] == 0 && !PrimeQ[#] && (! PrimeQ[# - 1] || !PrimeQ[# + 1]) & ]/2 (* G. C. Greubel, Jul 07 2016 *)

a(n) = A167692(n)/2.

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

Original entry on oeis.org

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

Rick L. Shepherd, Nov 13 2004

nonn

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

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

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.

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

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

[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

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

cp's OEIS Frontend

A168044 Half of the even nonisolated nonprimes A167692.

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