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

1,2

Links

Table of n, a(n) for n=1..105.

Formula

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

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

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 *)

Prog

(PARI) diff(v) = vector(#v-1, i, v[i+1]-v[i]);
lista(nn) = apply(x->(1<<valuation(x, 2)), diff(primes(nn))); \\ Michel Marcus, Aug 26 2019

Crossrefs

Cf. A006519, A001223, A023520.

Sequence in context: A227951 A102641 A054763 * A045841 A040003 A106469

Adjacent sequences: A100371 A100372 A100373 * A100375 A100376 A100377

Keyword

nonn

Author

Labos Elemer, Dec 03 2004

Status

approved