A219652 Number of steps to reach 0 starting with n and using the iterated process: x -> x - (sum of digits in factorial expansion of x).

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

Offset

0,3

Comments

See A007623 for the factorial number system representation.

Links

A. Karttunen, Table of n, a(n) for n = 0..10080

Formula

a(0)=0; for n>0, a(n) = 1 + a(A219651(n)).

Mathematica

nn = 72; m = 1; While[Factorial@ m < nn, m++]; m; Table[Length@ NestWhileList[# - Total@ IntegerDigits[#, MixedRadix[Reverse@ Range[2, m]]] &, n, # > 0 &] - 1, {n, 0, nn}] (* Michael De Vlieger, Jun 27 2016, Version 10.2 *)

Prog

(Scheme with memoization macro definec): (definec (A219652 n) (if (zero? n) n (+ 1 (A219652 (A219651 n)))))

Crossrefs

Analogous sequence for binary system: A071542, for Zeckendorf expansion: A219642. Cf. A007623, A034968, A219650, A219651, A219653-A219655, A219659, A219661, A219666.

Sequence in context: A303594 A085089 A228720 * A069924 A377028 A225559

Adjacent sequences: A219649 A219650 A219651 * A219653 A219654 A219655

Keyword

nonn,base

Author

Antti Karttunen, Nov 25 2012

Extensions

Erroneous description corrected by Antti Karttunen, Dec 03 2012

Status

approved