

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.


7



1, 2, 12, 108, 1944, 52488, 1102248, 44641044, 2008846980, 108477736920, 6508664215200, 421761441144960, 22142475660110400, 1793540528468942400, 160701231350817239040, 15909421903730906664960, 1874419162475932276162560
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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(n1). 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 1434digit 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



