

A305299


a(0) = 0, a(1) = 1, a(2) = 2; for n >= 2, a(2*n1) = n  2*a(n1)  1, a(2*n) = a(2*n1)  a(n).


2



0, 1, 2, 1, 3, 2, 1, 5, 8, 10, 12, 9, 10, 8, 3, 3, 11, 8, 18, 11, 23, 14, 23, 7, 17, 8, 16, 3, 6, 8, 11, 21, 32, 38, 46, 33, 51, 54, 65, 41, 64, 66, 80, 49, 72, 68, 75, 37, 54, 58, 66, 41, 57, 58, 61, 33, 39, 40, 32, 13, 2, 8, 13, 11, 43, 32, 70, 43, 89, 58, 91, 31, 82, 66, 120, 71, 136, 92
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OFFSET

0,3


COMMENTS

This sequence has an approximate selfsimilar block structure, which is roughly described by A110286, see Links section.
a(0) = 0 by definition. The next 0 is a(970) = 0. What are the other numbers k such that a(k) = 0?


LINKS

Robert Israel, Table of n, a(n) for n = 0..10000
Rémy Sigrist, Density plot of the first 16000000 terms
Altug Alkan, A scatterplot of a(n) for n <= 15*2^12
Altug Alkan, A scatterplot of a(n) for 15*2^12 <= n <= 15*2^14


MAPLE

f:= proc(n) option remember;
if n::odd then (n1)/22*procname((n1)/2)
else procname(n1)procname(n/2)
fi
end proc:
f(0):= 0: f(1):= 1: f(2):= 2:
map(f, [$0..77]); # after Robert Israel at A294044


MATHEMATICA

a[0] = 0; a[1] = 1; a[2] = 2; a[n_] := If[EvenQ[n], a[n  1]  a[n/2], (n  1)/2  2 a[(n  1)/2]]; Table[a[n], {n, 0, 77}] (* after Ilya Gutkovskiy at A294044 *)


PROG

(PARI) a(n)=if(n<=2, n, if(n%2==1, (n1)/22*a((n1)/2), a(n1)a(n/2)));
(PARI) a = vector(77); print1 (0", "); for (k=1, #a, print1 (a[k]=if (k<=2, k, my (n=k\2); if (k%2==0, a[2*n1]a[n], n2*a[n]))", ")) \\ after Rémy Sigrist at A303028


CROSSREFS

Cf. A002487, A294044, A303028.
Sequence in context: A152097 A119442 A064861 * A308701 A191528 A191788
Adjacent sequences: A305296 A305297 A305298 * A305300 A305301 A305302


KEYWORD

sign,look


AUTHOR

Altug Alkan, Aug 18 2018


STATUS

approved



