A065641 - OEIS

%I #23 Sep 03 2023 15:10:41

%S 0,1,10,60,90,101,120,380,450,505,807,1020,1070,1303,1450,3810,10020,

%T 10404,10560,16056,16200,18088,20322,20580,35790,79000,80088,90877,

%U 243700,279509,330832,374330,380038,903655,1002404,1005064,1020828

%N Smallest number with persistence n for the sort-and-subtract-sequence.

%C Sort the digits of an integer and subtract the result from the original. Continue with the result until you reach 0. The sequence gives the least integer that needs n steps to reach 0.

%H David W. Wilson and Reinhard Zumkeller, <a href="/A065641/b065641.txt">Table of n, a(n) for n = 0..100</a> (a(n) for n = 1..55 from Reinhard Zumkeller).

%e 60 is the smallest number that needs 3 steps to reach 0: 60 -> 60 - 06 = 54 -> 54 - 45 = 9 -> 9 - 9 = 0, hence a(3) = 60.

%t Persist[n_] := Length[NestWhileList[# - FromDigits[Sort[IntegerDigits[#]]] &, n, # != 0 &]] - 1; nn = 20; t = Table[0, {nn}]; cnt = 0; k = 0; While[cnt < nn, k++; c = Persist[k]; If[c <= nn && t[[c]] == 0, t[[c]] = k; cnt++]]; t  (* _Harvey P. Dale_, Mar 24 2011 *)

%t persist[n_]:=Length[NestWhileList[#-FromDigits[Sort[IntegerDigits[#]]]&,n,#!=0&]]-1; Module[ {nn=103*10^4,tbl},tbl=Table[{n,persist[n]},{n,0,nn}];DeleteDuplicates[ tbl,GreaterEqual[ #1[[2]],#2[[2]]]&]][[;;,1]] (* _Harvey P. Dale_, Sep 03 2023 *)

%o (Haskell)

%o import Data.List (elemIndex)

%o import Data.Maybe (fromJust)

%o a065641 n = a065641_list !! (n-1)

%o a065641_list = map (fromJust . (`elemIndex` a193582_list)) [1..]

%o -- _Reinhard Zumkeller_,Aug 10 2011

%Y Cf. A004185, A193582.

%K nonn,base,nice

%O 0,3

%A Ulrich Schimke (ulrschimke(AT)aol.com), Dec 03 2001

%E Added a(0) = 0. _David W. Wilson_, Jan 08 2017