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A160058 Primes whose distance to both nearest neighbor primes is not of the form 2^k.

%I A160058 #15 Feb 18 2019 01:55:32
%S A160058 53,157,173,211,251,257,263,293,331,337,373,509,541,547,557,563,577,
%T A160058 587,593,607,631,653,733,787,797,839,947,953,977,997,1039,1069,1103,
%U A160058 1123,1129,1181,1187,1223,1237,1249,1259,1327,1361,1367,1399,1409,1459,1471
%N A160058 Primes whose distance to both nearest neighbor primes is not of the form 2^k.
%C A160058 Intersection with A061771 yields an empty set. - _R. J. Mathar_, May 21 2009
%H A160058 Harvey P. Dale, <a href="/A160058/b160058.txt">Table of n, a(n) for n = 1..1000</a>
%H A160058 Klaus Lange, <a href="http://arxiv.org/abs/0904.4839">About a virtual subset</a>, Apr 30, 2009.
%p A160058 isA000079 := proc(n) if nops(numtheory[factorset](n)) > 1 then false; elif n mod 2 <> 0 then false; else true; fi; end: isA160058 := proc(p) o := prevprime(p) ; q := nextprime(p) ; if isprime(p) and not isA000079(q-p) and not isA000079(p-o) then true; else false; fi; end: for n from 2 to 1000 do p := ithprime(n) ; if isA160058(p) then printf("%d,",p) ; fi; od: # _R. J. Mathar_, May 21 2009
%t A160058 n2kQ[n_]:=Module[{d=Differences[n]},!IntegerQ[Log[2,First[d]]] && !IntegerQ[ Log[ 2,Last[d]]]]; Transpose[Select[Partition[Prime[ Range[ 300]],3,1],n2kQ]][[2]] (* _Harvey P. Dale_, Mar 05 2014 *)
%o A160058 (PARI) t=0;p=2;forprime(q=3,999, t*(t=q-p-1<<valuation(q-p,2)) & print1(p","); p=q)
%Y A160058 Cf. A000040. This is a proper subsequence of A137869.
%K A160058 nonn
%O A160058 1,1
%A A160058 _Jonathan Vos Post_, May 01 2009
%E A160058 More terms from _M. F. Hasler_, May 02 2008
%E A160058 Edited by _N. J. A. Sloane_, May 02 2009, based on comments from _M. F. Hasler_
%E A160058 More terms from _R. J. Mathar_, May 21 2009