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a(n) is the n-th consecutive prime difference divided by the largest power of 2 which divides it.
1

%I #11 Feb 20 2022 16:48:22

%S 1,1,1,1,1,1,1,1,3,1,3,1,1,1,3,3,1,3,1,1,3,1,3,1,1,1,1,1,1,7,1,3,1,5,

%T 1,3,3,1,3,3,1,5,1,1,1,3,3,1,1,1,3,1,5,3,3,3,1,3,1,1,5,7,1,1,1,7,3,5,

%U 1,1,3,1,3,3,1,3,1,1,1,5,1,5,1,3,1,3,1,1,1,1,3,1,1,1,1,3,3,1,9,3,5,3,3,1,3

%N a(n) is the n-th consecutive prime difference divided by the largest power of 2 which divides it.

%H Harvey P. Dale, <a href="/A100375/b100375.txt">Table of n, a(n) for n = 1..1000</a>

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

%t t1=Table[Prime[n+1]-Prime[n], {n, 1, 256}]; t2=Table[GCD[Prime[n+1]-Prime[n], 65536], {n, 1, 256}];t1/t2

%t #/2^IntegerExponent[#,2]&/@Differences[Prime[Range[110]]] (* _Harvey P. Dale_, Feb 20 2022 *)

%Y Cf. A006519, A001223, A100374.

%K nonn

%O 1,9

%A _Labos Elemer_, Dec 03 2004