A061771 -id:A061771 - cp's OEIS frontend

A082508 Differences between consecutive primes that are powers of 2 in order of their appearance. Differences that are not powers of 2 are deleted from A001223.

1, 2, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 8, 4, 2, 4, 2, 4, 4, 2, 2, 4, 2, 2, 4, 2, 4, 2, 4, 2, 2, 4, 2, 4, 2, 4, 2, 4, 8, 4, 8, 4, 8, 2, 2, 4, 8, 4, 2, 4, 8, 4, 8, 4, 2, 2, 2, 4, 2, 2, 4, 2, 4, 8, 8, 8, 4, 8, 4, 8, 4, 2, 2, 4, 2, 4, 2, 4, 4, 2, 4, 4, 8, 8, 4, 4, 8, 4, 2, 2, 2, 2, 4, 2, 4, 8, 2, 8, 8, 4, 2

Offset: 1

Labos Elemer, Apr 28 2003

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A001223, A061771.

Do[s=Log[2, Prime[n+1]-Prime[n]]; If[IntegerQ[s], Print[Prime[n+1]]], {n, 1, 1000}]

lista(pmax) = {my(p1 = 2, gap); forprime(p2 = 3, pmax, gap = p2 - p1; if(gap >> valuation(gap, 2) == 1, print1(gap, ", ")); p1 = p2);} \\ Amiram Eldar, Jun 06 2024

a(n) = A001223(A061771(n)). - Amiram Eldar, Jun 06 2024

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

Original entry on oeis.org

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

Offset: 1

Jonathan Vos Post, May 01 2009

nonn

Intersection with A061771 yields an empty set. - R. J. Mathar, May 21 2009

Harvey P. Dale, Table of n, a(n) for n = 1..1000
Klaus Lange, About a virtual subset, Apr 30, 2009.

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

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

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 *)

t=0;p=2;forprime(q=3,999, t*(t=q-p-1<

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

cp's OEIS Frontend

A082508 Differences between consecutive primes that are powers of 2 in order of their appearance. Differences that are not powers of 2 are deleted from A001223.

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