A082508 -id:A082508 - cp's OEIS frontend

A082509 Differences between consecutive primes that are not powers of 2 in order of their appearance. Differences which are powers of 2 are omitted from A001223.

6, 6, 6, 6, 6, 6, 6, 14, 6, 10, 6, 6, 6, 6, 10, 12, 12, 6, 10, 6, 6, 6, 6, 10, 14, 14, 6, 10, 6, 6, 6, 6, 10, 10, 6, 6, 12, 6, 12, 18, 6, 10, 6, 6, 6, 10, 6, 6, 6, 6, 12, 10, 6, 6, 12, 6, 10, 10, 6, 6, 6, 14, 10, 12, 10, 10, 14, 14, 20, 10, 6, 6, 14, 6, 6, 6, 12, 6, 10, 6, 10, 10, 6, 18, 6, 6, 6

Offset: 1

Labos Elemer, Apr 28 2003

nonn

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

Cf. A001223, A082508.

Do[s=Log[2, Prime[n+1]-Prime[n]]; If[ !IntegerQ[s], Print[Prime[n+1]]], {n, 1, 1000}]
Module[{nn=250,twos},twos=2^Range[0,Floor[Log[2,Prime[nn]]]];Select[ Differences[ Prime[Range[nn]]],!MemberQ[twos,#]&]] (* Harvey P. Dale, Apr 18 2012 *)

list(lim) = {my(p = 2, d); forprime(q = 3, lim, d = q - p; if(d >> valuation(d, 2) > 1, print1(d, ", ")); p = q);} \\ Amiram Eldar, Feb 16 2025

A130796 Primes p such that nextprime(p)-p is not power of 2.

Original entry on oeis.org

23, 31, 47, 53, 61, 73, 83, 113, 131, 139, 151, 157, 167, 173, 181, 199, 211, 233, 241, 251, 257, 263, 271, 283, 293, 317, 331, 337, 353, 367, 373, 383, 409, 421, 433, 443, 467, 503, 509, 523, 541, 547, 557, 563, 571, 577, 587, 593, 601, 607, 619, 631, 647

Offset: 1

Zak Seidov, Aug 20 2007

nonn

Indices of primes are 9,11,15,16,18,21,23,30,32,34,36,37,39,40,42,46,47,51, 53,54,55,56,58,61,62,66,... (subsequence of A113339).

Cf. A001223 Differences between consecutive primes, A082509 Differences between consecutive primes that are not powers of 2, A082508 Differences between consecutive primes that are powers of 2, A113339 Integers n such that prime(n+1)-prime(n) is nonprime, squarefree.

Mathematica
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<Harvey P. Dale, Apr 20 2011 *)
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A082510 Differences of consecutive primes being divisible by 6 in order of their appearance in A001223: terms not divisible by 6 are omitted from A001223.

Original entry on oeis.org

6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 12, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 6, 12, 18, 6, 6, 6, 6, 6, 6, 6, 6, 12, 6, 6, 12, 6, 6, 6, 6, 12, 6, 6, 6, 6, 6, 12, 6, 6, 6, 18, 6, 6, 6, 6, 6, 6, 12, 6, 6, 6, 12, 18, 6, 6, 12, 6, 6, 6, 18, 6, 6, 12, 6, 12, 12, 12, 6, 6, 6, 6, 6, 6, 24, 12, 6, 6, 6, 18

Offset: 1

Labos Elemer, Apr 28 2003

nonn

Cf. A001223, A082508, A082509.

Do[s=Mod[d=Prime[n+1]-Prime[n], 6]; If[Equal[s, 0], Print[d]], {n, 1, 1000}]
Select[Last[#]-First[#]&/@Partition[Prime[Range[500]],2,1], Divisible[ #,6]&] (* Harvey P. Dale, Mar 18 2012 *)
Select[Differences[Prime[Range[500]]],Divisible[#,6]&] (* Harvey P. Dale, May 13 2020 *)

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A082509 Differences between consecutive primes that are not powers of 2 in order of their appearance. Differences which are powers of 2 are omitted from A001223.

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A130796 Primes p such that nextprime(p)-p is not power of 2.

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A082510 Differences of consecutive primes being divisible by 6 in order of their appearance in A001223: terms not divisible by 6 are omitted from A001223.

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