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

Author

Max Alekseyev, Jul 22 2019

Keywords

• base
• nonn

Comments

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

Links

• International Mathematical Olympiad, Problem 5 of IMO 2019.
• Rémy Sigrist, Scatterplot of the ordinal transform of the first 2^16 terms

Crossrefs

Cf. A000120, A326729, A326730, A326731.

Programs

PARI

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

Formula

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

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