A292246 Base-2 expansion of a(n) encodes the steps where numbers of the form 3k+2 are encountered when map x -> A253889(x) is iterated down to 1, starting from x=n.

0, 1, 0, 2, 3, 0, 4, 1, 2, 14, 5, 12, 6, 7, 8, 2, 1, 0, 0, 9, 26, 22, 3, 20, 6, 5, 16, 10, 29, 10, 4, 11, 30, 2, 25, 60, 56, 13, 28, 54, 15, 48, 24, 17, 44, 8, 5, 12, 38, 3, 30, 26, 1, 24, 20, 1, 18, 6, 19, 62, 14, 53, 4, 14, 45, 0, 42, 7, 124, 118, 41, 50, 58, 13, 116, 106, 11, 40, 104, 33, 32, 98, 21, 92, 6, 59, 88, 18, 21, 82, 76, 9, 34, 36, 23, 74

Offset: 1

Author

Antti Karttunen, Sep 15 2017

Keywords

• nonn
• base

Examples

			For n = 2, the starting value is of the form 3k+2, after which follows A253889(3) = 1, the end point of iteration, which is not, thus a(2) = 1*(2^0) = 1.
For n = 4, the starting value is not of the form 3k+2, while A253889(4) = 2 is, thus a(4) = 0*(2^0) + 1*(2^1) = 2.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for sequences related to binary expansion of n
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A064216, A253889, A254045, A289814, A292243, A292244, A292245.

Cf. also A291759.

Programs

Mathematica

f[n_] := Times @@ Power[If[# == 1, 1, NextPrime[#, -1]] & /@ First@ #, Last@ #] &@ Transpose@ FactorInteger[2 n - 1]; g[n_] := (Times @@ Power[If[# == 1, 1, NextPrime@ #] & /@ First@ #, Last@ #] + 1)/2 &@ Transpose@ FactorInteger@ n; Map[FromDigits[#, 2] &[IntegerDigits[#, 3] /. d_ /; d > 0 :> d - 1] &, Array[a, 96]] (* Michael De Vlieger, Sep 16 2017 *)

Formula

a(1) = 0; for n > 1, a(n) = 2*a(A253889(n)) + floor((n mod 3)/2).

a(n) = A289814(A292243(n)).

A000120(a(n)) = A254045(n).

a(n) AND A292244(n) = a(n) AND A292245(n) = 0, where AND is a bitwise-AND (A004198).