A100374 Largest power of 2 dividing prime(n+1) - prime(n), the n-th consecutive prime difference.

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

Offset: 1

Author

Labos Elemer, Dec 03 2004

Keywords

• nonn

Links

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

Crossrefs

Cf. A006519, A001223, A023520.

Programs

Mathematica

Table[GCD[Prime[n+1]-Prime[n], 65536], {n, 1, 256}] (* a secure quick code *)
2^IntegerExponent[#,2]&/@Flatten[Differences/@Partition[Prime[Range[ 110]],2,1]] (* Harvey P. Dale, Apr 28 2012 *)

PARI

diff(v) = vector(#v-1, i, v[i+1]-v[i]);
lista(nn) = apply(x->(1<Michel Marcus, Aug 26 2019

Formula

a(n) = A006519(A001223(n)).

a(n) = 2^A023520(n). - Michel Marcus, Aug 26 2019