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%I #13 Jul 07 2016 04:27:24
%S 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,
%T 32,33,34,35,36,38,39,40,41,43,44,45,46,48,49,50,51,52,54,55,56,57,58,
%U 59,61,62,63,64,65,66,68,69,70,71,73,74,75,76,77,78,80,81,82,84,85,86,87
%N The non-single or nonisolated numbers. The union of non-single (or nonisolated or twin) primes and non-single (or nonisolated) nonprimes.
%C A167707 = A001097 U A164276. A167706 U A167707 = A001477.
%H G. C. Greubel, <a href="/A167707/b167707.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = n + n / log n + O(n / (log n)^2) by Brun's theorem. [_Charles R Greathouse IV_, Mar 15 2011]
%p 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
%t Union[Select[Range[0, 300], !PrimeQ[#] && (! PrimeQ[# - 1] || ! PrimeQ[# + 1]) & ], Select[Prime[Range[300]], PrimeQ[# - 2] || PrimeQ[# + 2] &]] (* _G. C. Greubel_, Jul 07 2016 *)
%Y Cf. A001097, A001477, A164276, A167706.
%K nonn
%O 1,3
%A _Juri-Stepan Gerasimov_, Nov 10 2009
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