A261231 - OEIS

A261231

a(n) = number of steps to reach 0 when starting from k = n and repeatedly applying the map that replaces k with k - (sum of digits in base-3 representation of k).

0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 19, 20, 20, 20, 20, 20, 20, 21, 21, 21, 22, 22, 22, 23, 23, 23, 24, 24, 24

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..19683

FORMULA

a(0) = 0; for n >= 1, a(n) = 1 + a(2*A054861(n)). [Note that A054861(n) = (n - A053735(n))/2, where A053735(n) = sum of digits of n, when written in base 3.]

PROG

(Scheme, with memoization-macro definec)

(definec (A261231 n) (if (zero? n) n (+ 1 (A261231 (* 2 (A054861 n))))))

(Python)

from sympy.ntheory.factor_ import digits

def a054861(n): return (n - sum(digits(n, 3)[1:]))/2

def a(n): return 0 if n==0 else 1 + a(2*a054861(n)) # Indranil Ghosh, May 22 2017

CROSSREFS

Cf. A000244, A053735, A054861, A261232, A261233, A261234, A261235.

Cf. also A071542.

Sequence in context: A172264 A079001 A032615 * A296357 A002264 A086161

Adjacent sequences: A261228 A261229 A261230 * A261232 A261233 A261234

KEYWORD

nonn

AUTHOR

Antti Karttunen, Aug 12 2015

STATUS

approved