

A292246


Base2 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.


6



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
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OFFSET

1,4


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(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 bitwiseAND (A004198).


EXAMPLE

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.


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 *)


PROG

(Scheme, with memoizationmacro definec)
(definec (A292246 n) (if (= 1 n) 0 (+ (floor>exact (/ (modulo n 3) 2)) (* 2 (A292246 (A253889 n))))))


CROSSREFS

Cf. A064216, A253889, A254045, A289814, A292243, A292244, A292245.
Cf. also A291759.
Sequence in context: A014197 A341825 A181308 * A277141 A021438 A195822
Adjacent sequences: A292243 A292244 A292245 * A292247 A292248 A292249


KEYWORD

nonn,base


AUTHOR

Antti Karttunen, Sep 15 2017


STATUS

approved



