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A160058
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Primes whose distance to both nearest neighbor primes is not of the form 2^k.
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1
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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
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listen;
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OFFSET
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1,1
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COMMENTS
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Intersection with A061771 yields an empty set. - R. J. Mathar, May 21 2009
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LINKS
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Harvey P. Dale, Table of n, a(n) for n = 1..1000
Klaus Lange, About a virtual subset, Apr 30, 2009.
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MAPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(PARI) t=0; p=2; forprime(q=3, 999, t*(t=q-p-1<<valuation(q-p, 2)) & print1(p", "); p=q)
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CROSSREFS
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Cf. A000040. This is a proper subsequence of A137869.
Sequence in context: A044385 A044766 A342450 * A353136 A053070 A140655
Adjacent sequences: A160055 A160056 A160057 * A160059 A160060 A160061
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KEYWORD
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nonn
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AUTHOR
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Jonathan Vos Post, May 01 2009
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EXTENSIONS
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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
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STATUS
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approved
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