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Length of longest contiguous block of 0's in binary expansion of n-th prime.
4

%I #6 Jul 19 2015 01:29:16

%S 1,0,1,0,1,1,3,2,1,1,0,2,2,1,1,1,1,1,4,3,2,2,2,2,4,2,2,1,1,3,0,5,3,3,

%T 2,2,2,3,2,1,2,1,1,5,3,3,2,1,3,2,2,1,3,1,7,5,4,4,3,3,3,2,2,2,2,2,2,3,

%U 1,1,4,2,1,1,1,1,4,3,3,2,3,2,1,3,1,1,5,2,2,2,2,1,2,1,2,1,1,5,5,4,3,3,3,3,3

%N Length of longest contiguous block of 0's in binary expansion of n-th prime.

%C a(n) = A087117(A000040(n)).

%t f[n_] := Length[ Union[ DeleteCases[ Split[ IntegerDigits[n, 2]], 1, 2]][[ -1]]]; Table[ f[ Prime[n]], {n, 1, 105}] (* _Robert G. Wilson v_, Dec 03 2003 *)

%Y Cf. A023416, A004676, A090047, A090048, A090049, A090000.

%K nonn,base

%O 1,7

%A _Reinhard Zumkeller_, Nov 20 2003