A167707 The non-single or nonisolated numbers. The union of non-single (or nonisolated or twin) primes and non-single (or nonisolated) nonprimes.

0, 1, 3, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 38, 39, 40, 41, 43, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87

Offset: 1

Author

Juri-Stepan Gerasimov, Nov 10 2009

Keywords

• nonn

Comments

A167707 = A001097 U A164276. A167706 U A167707 = A001477.

Links

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

Crossrefs

Cf. A001097, A001477, A164276, A167706.

Programs

Maple

isA001097 := proc(n) isprime(n) and (isprime(n+2) or isprime(n-2)) ; end proc: isA164276 := proc(n) not isprime(n) and ( not isprime(n+1) or not isprime(n-1) ) ; end proc: isA167707 := proc(n) isA001097(n) or isA164276(n) ; end proc: for n from 0 to 100 do if isA167707(n) then printf("%d,",n) ; end if; end do: # R. J. Mathar, Mar 18 2010

Mathematica

Union[Select[Range[0, 300], !PrimeQ[#] && (! PrimeQ[# - 1] || ! PrimeQ[# + 1]) & ], Select[Prime[Range[300]], PrimeQ[# - 2] || PrimeQ[# + 2] &]] (* G. C. Greubel, Jul 07 2016 *)

Formula

a(n) = n + n / log n + O(n / (log n)^2) by Brun's theorem. [Charles R Greathouse IV, Mar 15 2011]