A292244 Base-2 expansion of a(n) encodes the steps where multiples of 3 are encountered when map x -> A253889(x) is iterated down to 1, starting from x=n.

0, 0, 1, 0, 0, 3, 0, 2, 5, 0, 0, 1, 0, 0, 1, 12, 6, 7, 14, 0, 1, 0, 4, 1, 8, 10, 3, 0, 0, 21, 24, 0, 1, 28, 2, 3, 2, 0, 1, 0, 0, 5, 2, 2, 1, 22, 24, 17, 0, 12, 33, 32, 14, 35, 42, 28, 45, 24, 0, 1, 16, 2, 11, 48, 0, 59, 0, 8, 3, 0, 2, 5, 0, 16, 1, 4, 20, 3, 6, 6, 7, 8, 0, 1, 56, 0, 3, 0, 42, 5, 0, 48, 5, 0, 0, 1, 14, 2, 65, 64, 56, 49, 44, 4, 49, 64, 6, 57, 0

Offset

1,6

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

Formula

a(n) = A291770(A292243(n)).

Other identities. For all n >= 1:

a(A048673(n)) = A292247(n).

a(n) + A292245(n) = A064216(n).

a(n) AND A292245(n) = a(n) AND A292246(n) = 0, where AND is a bitwise-AND (A004198).

Example

For n = 3, the starting value is a multiple of three, after which follows A253889(3) = 1, the end point of iteration, which is not a multiple of three, thus a(3) = 1*(2^0) = 1.
For n = 8, the starting value is not a multiple of three, after which follows A253889(8) = 3, which is, thus a(8) = 0*(2^0) + 1*(2^1) = 2.
For n = 9, the starting value is a multiple of three, after which follows A253889(9) = 8 (which is not), while A253889(8) = 3 (which is), thus a(9) = 1*(2^0) + 0*(2^1) + 1*(2^2) = 5.

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; Table[FromDigits[#, 2] &@ Map[Boole[Divisible[#, 3]] &,  Reverse@ NestWhileList[Floor@ g[Floor[f[#]/2]] &, n, # > 1 &]], {n, 109}] (* Michael De Vlieger, Sep 16 2017 *)

Prog

(Scheme) (define (A292244 n) (A291770 (A292243 n)))

Crossrefs

Cf. A048673, A064216, A253889, A291770, A292243, A292247.

Cf. also A292245, A292246, and A292381, A292383, A292385, and A292590, A292591 for similarly constructed sequences, and also A292250.

Sequence in context: A273084 A349728 A261163 * A208329 A283025 A089598

Adjacent sequences: A292241 A292242 A292243 * A292245 A292246 A292247

Keyword

nonn,base,look

Author

Antti Karttunen, Sep 15 2017

Status

approved