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A160058 Primes whose distance to both nearest neighbor primes is not of the form 2^k. 1

%I #15 Feb 18 2019 01:55:32

%S 53,157,173,211,251,257,263,293,331,337,373,509,541,547,557,563,577,

%T 587,593,607,631,653,733,787,797,839,947,953,977,997,1039,1069,1103,

%U 1123,1129,1181,1187,1223,1237,1249,1259,1327,1361,1367,1399,1409,1459,1471

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

%C Intersection with A061771 yields an empty set. - _R. J. Mathar_, May 21 2009

%H Harvey P. Dale, <a href="/A160058/b160058.txt">Table of n, a(n) for n = 1..1000</a>

%H Klaus Lange, <a href="http://arxiv.org/abs/0904.4839">About a virtual subset</a>, Apr 30, 2009.

%p 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 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 (PARI) t=0;p=2;forprime(q=3,999, t*(t=q-p-1<<valuation(q-p,2)) & print1(p","); p=q)

%Y Cf. A000040. This is a proper subsequence of A137869.

%K nonn

%O 1,1

%A _Jonathan Vos Post_, May 01 2009

%E More terms from _M. F. Hasler_, May 02 2008

%E Edited by _N. J. A. Sloane_, May 02 2009, based on comments from _M. F. Hasler_

%E More terms from _R. J. Mathar_, May 21 2009

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Last modified March 29 09:59 EDT 2024. Contains 371268 sequences. (Running on oeis4.)