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

Author

Labos Elemer, Apr 28 2003

Keywords

• nonn

Links

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

Crossrefs

Cf. A001223, A061771.

Programs

Mathematica

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

PARI

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

Formula

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