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A160058 Primes whose distance to both nearest neighbor primes is not of the form 2^k. 1
53, 157, 173, 211, 251, 257, 263, 293, 331, 337, 373, 509, 541, 547, 557, 563, 577, 587, 593, 607, 631, 653, 733, 787, 797, 839, 947, 953, 977, 997, 1039, 1069, 1103, 1123, 1129, 1181, 1187, 1223, 1237, 1249, 1259, 1327, 1361, 1367, 1399, 1409, 1459, 1471 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Intersection with A061771 yields an empty set. [From R. J. Mathar, May 21 2009]

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Klaus Lange, About a virtual subset, Apr 30, 2009.

MAPLE

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: [From R. J. Mathar, May 21 2009]

MATHEMATICA

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 *)

PROG

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

CROSSREFS

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

Sequence in context: A217718 A044385 A044766 * A053070 A140655 A142508

Adjacent sequences:  A160055 A160056 A160057 * A160059 A160060 A160061

KEYWORD

nonn

AUTHOR

Jonathan Vos Post, May 01 2009

EXTENSIONS

More terms from M. F. Hasler, May 02 2008

Edited by N. J. A. Sloane, May 02 2009, based on comments from M. F. Hasler

More terms from R. J. Mathar, May 21 2009

STATUS

approved

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Last modified October 24 06:43 EDT 2017. Contains 293836 sequences.