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2-adic valuation of A123581(2*n).
2

%I #16 Dec 07 2023 08:27:58

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

%T 2,1,3,1,3,1,1,2,1,2,1,4,1,2,4,1,2,1,3,1,1,3,1,2,2,1,6,1,1,6,1,2,1,2,

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

%N 2-adic valuation of A123581(2*n).

%C A123581(n) is odd if n is odd.

%H N. J. A. Sloane, <a href="/A367624/b367624.txt">Table of n, a(n) for n = 1..5000</a>

%t With[{nmax=100},IntegerExponent[NestList[#+FactorInteger[#][[-1,1]]&,3,2nmax-1][[2;;-1;;2]],2]] (* _Paolo Xausa_, Dec 07 2023 *)

%Y Cf. A007814, A123581.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Dec 06 2023