A057525 Number of applications of f to reduce n to 1, where f(k) is the integer among k/2,(k+1)/4, (k+3)/4.

1, 1, 2, 2, 2, 2, 3, 2, 3, 2, 3, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 4, 3, 4, 4, 4, 4, 5, 3, 4, 3, 4, 4, 4, 4, 5, 3, 4, 3, 4, 4, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4, 5, 4, 5, 4, 5, 5, 5, 5, 6, 4, 4, 4, 5, 4, 4, 4, 5, 4, 5, 4, 5, 5, 5, 5, 6, 4, 4, 4, 5, 4, 4, 4, 5, 4, 5, 4

Offset

2,3

Comments

Alternatively, a(n+1) is the number of periods of the prefix of length n of the period-doubling word (A035263). - Jeffrey Shallit, May 19 2020

Alternatively, a(n+1) is the length of the (unique factorization) of the base-2 representation of n into the blocks 1, 00, and 10. - Jeffrey Shallit, May 19 2020

Links

Table of n, a(n) for n=2..91.

Example

a(11)=3, which counts these reductions: 11->4->2->1.

Crossrefs

Cf. A035263.

Sequence in context: A108502 A260235 A078120 * A331362 A139325 A341829

Adjacent sequences: A057522 A057523 A057524 * A057526 A057527 A057528

Keyword

nonn

Author

Clark Kimberling, Sep 03 2000

Status

approved