A292593 a(n) = A292591(A245612(n)).

0, 1, 2, 2, 4, 5, 4, 5, 8, 8, 10, 11, 8, 8, 10, 10, 16, 17, 16, 17, 20, 20, 22, 23, 16, 17, 16, 16, 20, 21, 20, 21, 32, 32, 34, 35, 32, 32, 34, 34, 40, 41, 40, 41, 44, 44, 46, 47, 32, 32, 34, 34, 32, 33, 32, 32, 40, 40, 42, 43, 40, 40, 42, 42, 64, 65, 64, 65, 68, 68, 70, 71, 64, 65, 64, 64, 68, 69, 68, 69, 80, 80, 82, 83, 80, 80, 82, 82, 88, 89, 88, 89

Offset: 0

Author

Antti Karttunen, Sep 20 2017

Keywords

• nonn
• base

Links

• Antti Karttunen, Table of n, a(n) for n = 0..8191
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A245612, A292591, A292592.

Differs from A292271 for the first time at n=31, where a(31) = 21, while A292271(31) = 20.

Programs

Mathematica

f[n_] := f[n] = Which[n == 1, 0, Mod[n, 3] == 2, Ceiling[n/3], True, (Times @@ Power[If[# == 1, 1, NextPrime[#, -1]] & /@ First@ #, Last@ #] &@ Transpose@ FactorInteger[2 n - 1] + 1)/2]; g[n_] := g[n] = If[n <= 2, n - 1, 2 g[f@ n] + Boole[Mod[n, 3] == 1]]; h[n_] := (Times @@ Power[If[# == 1, 1, NextPrime@ #] & /@ First@ #, Last@ #] + 1)/2 &@ Transpose@ FactorInteger@ If[n == 0, 1, Prime[#] Product[Prime[m]^(Map[ Ceiling[ (Length@ # - 1)/2] &, DeleteCases[Split@ Join[Riffle[IntegerDigits[n, 2], 0], {0}], {k__} /; k == 1]][[-m]]), {m, #}] &[DigitCount[n, 2, 1]]]; Array[g@ h@ # &, 92, 0] (* Michael De Vlieger, Sep 22 2017 *)

Formula

a(n) + A292592(n) = n.