A235601 Smallest number m such that repeated application of A235600 takes n steps to reach 1, where A235600(k) = k/A007953(k) if the digital sum A007953(k) divides k, A235600(k) = k otherwise.

1, 2, 12, 108, 1944, 52488, 1102248, 44641044, 2008846980, 108477736920, 6508664215200, 421761441144960, 22142475660110400, 1793540528468942400, 160701231350817239040, 15909421903730906664960, 1874419162475932276162560

Offset

0,2

Comments

Numbers m > 1 which never reach 1 are not candidates for a(n).

There is no analog in base 2 (cf. A235602).

Comment from David W. Wilson, Jan 20 2013: let S(0) = {1}; for each n >= 1, compute the set S(n) of possible predecessors of elements of S(n-1). Then a(n) is the smallest element of S(n). Using this approach, I was able to compute up to a(100).

The sequence is finite with a(440), a 1434-digit number being the final term. - Hans Havermann and Ray Chandler, Jan 21 2014

Sequence A236338 gives the count of iterations of A235600 required to reach 1 when starting from any n. Otherwise said: This sequence is the RECORDS transform of A236338. - M. F. Hasler, Jan 22 2014

The terms are a proper subset of A114440. - Robert G. Wilson v, Jan 22 2014

Links

Hans Havermann and Ray Chandler, Table of n, a(n) for n = 0..440 [First 100 terms were computed by David W. Wilson]

Example

a(4) = 1944: 1944 ->1944/18 = 108 -> 108/9 = 12 -> 12/3 = 4 -> 4/4 = 1 in 4 steps.

Mathematica

s={1}; Print[s[[1]]]; Do[t={}; Do[v=s[[k]]; u={}; Do[If[Total[IntegerDigits[c*v]]==c, AppendTo[u, c*v]], {c, 2, 7000}]; t=Join[t, u], {k, Length[s]}]; s=Sort[t]; Print[s[[1]]], {440}] (* Hans Havermann, Jan 21 2014 *)

Crossrefs

Cf. A005349, A007953, A114440, A235600, A236385.

Sequence in context: A339301 A179493 A193268 * A007724 A217800 A241958

Adjacent sequences: A235598 A235599 A235600 * A235602 A235603 A235604

Keyword

nonn,base,fini,full

Author

N. J. A. Sloane and David W. Wilson, Jan 18 2014

Extensions

a(8) from Hans Havermann, Jan 19 2014

a(9)-a(100) from David W. Wilson, Jan 21 2014

a(101)-a(440) from Hans Havermann and Ray Chandler, Jan 21 2014

Status

approved