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

1,3

Comments

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

Links

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

Formula

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

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 *)

Crossrefs

Cf. A001097, A001477, A164276, A167706.

Sequence in context: A217129 A336340 A100318 * A131903 A141114 A136443

Adjacent sequences: A167704 A167705 A167706 * A167708 A167709 A167710

Keyword

nonn

Author

Juri-Stepan Gerasimov, Nov 10 2009

Status

approved