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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. 0
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 (list; graph; refs; listen; history; text; internal format)
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 A216325

Adjacent sequences:  A057522 A057523 A057524 * A057526 A057527 A057528

KEYWORD

nonn

AUTHOR

Clark Kimberling, Sep 03 2000

STATUS

approved

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Last modified September 30 22:26 EDT 2020. Contains 337440 sequences. (Running on oeis4.)