A326732 Number of iterations of A326731(x) starting at x = n to reach 0.

0, 1, 1, 2, 1, 4, 2, 3, 1, 6, 4, 7, 2, 5, 3, 4, 1, 8, 6, 11, 4, 9, 7, 10, 2, 7, 5, 8, 3, 6, 4, 5, 1, 10, 8, 15, 6, 13, 11, 16, 4, 11, 9, 14, 7, 12, 10, 13, 2, 9, 7, 12, 5, 10, 8, 11, 3, 8, 6, 9, 4, 7, 5, 6, 1, 12, 10, 19, 8, 17, 15, 22, 6, 15, 13, 20, 11, 18, 16, 21, 4, 13, 11, 18, 9, 16, 14, 19, 7, 14, 12, 17, 10, 15, 13, 16, 2, 11, 9, 16, 7

Offset

0,4

Comments

The sequence is well-defined, see Problem 5 of IMO 2019.

Links

Table of n, a(n) for n=0..100.

International Mathematical Olympiad, Problem 5 of IMO 2019.

Rémy Sigrist, Scatterplot of the ordinal transform of the first 2^16 terms

Formula

a(n) = 2*A230877(n) - A000120(n)^2.

a(n) = 1 iff n is a power of 2.

Prog

(PARI) A326732(n) = my(b=binary(n)); 2*sum(i=1, #b, i*b[i]) - vecsum(b)^2;

Crossrefs

Cf. A000120, A326729, A326730, A326731.

Sequence in context: A078458 A033317 A183200 * A305422 A007733 A128520

Adjacent sequences: A326729 A326730 A326731 * A326733 A326734 A326735

Keyword

base,nonn

Author

Max Alekseyev, Jul 22 2019

Status

approved