A100374 - OEIS

%I #16 Dec 12 2021 20:10:52

%S 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,

%T 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,

%U 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

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

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

%F a(n) = 2^A023520(n). - _Michel Marcus_, Aug 26 2019

%t Table[GCD[Prime[n+1]-Prime[n], 65536], {n, 1, 256}] (* a secure quick code *)

%t 2^IntegerExponent[#,2]&/@Flatten[Differences/@Partition[Prime[Range[ 110]],2,1]] (* _Harvey P. Dale_, Apr 28 2012 *)

%o (PARI) diff(v) = vector(#v-1, i, v[i+1]-v[i]);

%o lista(nn) = apply(x->(1<<valuation(x, 2)), diff(primes(nn))); \\ _Michel Marcus_, Aug 26 2019

%Y Cf. A006519, A001223, A023520.

%K nonn

%O 1,2

%A _Labos Elemer_, Dec 03 2004