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a(n) = 2*n + 1 + valuation(n, 2) with valuation(n, 2) = A007814(n).
3

%I #13 Mar 25 2022 18:26:28

%S 3,6,7,11,11,14,15,20,19,22,23,27,27,30,31,37,35,38,39,43,43,46,47,52,

%T 51,54,55,59,59,62,63,70,67,70,71,75,75,78,79,84,83,86,87,91,91,94,95,

%U 101,99,102,103,107,107,110,111,116,115,118,119,123,123,126

%N a(n) = 2*n + 1 + valuation(n, 2) with valuation(n, 2) = A007814(n).

%C Duplicated terms 11, 27, 43, 59, ... are A106839 (verified with 1000 terms). - _Jean-François Alcover_, Sep 24 2017 (comment made further to an e-mail from Paul Curtz)

%p a := n -> 2*n + 1 + padic:-ordp(n, 2): seq(a(n), n=1..62);

%t a[n_] := 2n + 1 + IntegerExponent[n, 2]; Array[a, 62]

%o (PARI) a(n) = 2*n+1+valuation(n, 2); \\ _Michel Marcus_, Sep 25 2017

%Y Cf. A007814, A106839.

%K nonn

%O 1,1

%A _Peter Luschny_, Sep 23 2017