A292246 - OEIS

%I #14 Sep 18 2017 09:23:32

%S 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,

%T 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,

%U 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

%N 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.

%H Antti Karttunen, <a href="/A292246/b292246.txt">Table of n, a(n) for n = 1..16384</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

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

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

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

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

%e 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.

%e 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.

%t 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 *)

%o (Scheme, with memoization-macro definec)

%o (definec (A292246 n) (if (= 1 n) 0 (+ (floor->exact (/ (modulo n 3) 2)) (* 2 (A292246 (A253889 n))))))

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

%Y Cf. also A291759.

%K nonn,base

%O 1,4

%A _Antti Karttunen_, Sep 15 2017