cp's OEIS Frontend

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.

%I A235601 #51 Dec 23 2024 15:54:37
%S A235601 1,2,12,108,1944,52488,1102248,44641044,2008846980,108477736920,
%T A235601 6508664215200,421761441144960,22142475660110400,1793540528468942400,
%U A235601 160701231350817239040,15909421903730906664960,1874419162475932276162560
%N 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.
%C A235601 Numbers m > 1 which never reach 1 are not candidates for a(n).
%C A235601 There is no analog in base 2 (cf. A235602).
%C A235601 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).
%C A235601 The sequence is finite with a(440), a 1434-digit number being the final term. - _Hans Havermann_ and _Ray Chandler_, Jan 21 2014
%C A235601 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
%C A235601 The terms are a proper subset of A114440. - _Robert G. Wilson v_, Jan 22 2014
%H A235601 Hans Havermann and Ray Chandler, <a href="/A235601/b235601.txt">Table of n, a(n) for n = 0..440</a> [First 100 terms were computed by David W. Wilson]
%H A235601 David W. Wilson, Ray Chandler, Alonso Del Arte, M. F. Hasler, Hans Havermann, Alex Meiburg, N. J. A. Sloane, Hugo Van Der Sanden, and Allan Wechsler, <a href="/A235601/a235601.txt">As much as I hate "base" sequences...</a>, Copies of various posts to the Sequence Fans Mailing List, Circa January 2014. Assembled by _N. J. A. Sloane_, Dec 23 2024
%e A235601 a(4) = 1944: 1944 ->1944/18 = 108 -> 108/9 = 12 -> 12/3 = 4 -> 4/4 = 1 in 4 steps.
%t A235601 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 *)
%Y A235601 Cf. A005349, A007953, A114440, A235600, A236385.
%K A235601 nonn,base,fini,full
%O A235601 0,2
%A A235601 _N. J. A. Sloane_ and _David W. Wilson_, Jan 18 2014
%E A235601 a(8) from _Hans Havermann_, Jan 19 2014
%E A235601 a(9)-a(100) from _David W. Wilson_, Jan 21 2014
%E A235601 a(101)-a(440) from _Hans Havermann_ and _Ray Chandler_, Jan 21 2014