A065641 Smallest number with persistence n for the sort-and-subtract-sequence.

0, 1, 10, 60, 90, 101, 120, 380, 450, 505, 807, 1020, 1070, 1303, 1450, 3810, 10020, 10404, 10560, 16056, 16200, 18088, 20322, 20580, 35790, 79000, 80088, 90877, 243700, 279509, 330832, 374330, 380038, 903655, 1002404, 1005064, 1020828

Offset: 0

Author

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

Keywords

• nonn
• base
• nice

Comments

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.

Examples

			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.
		

Links

• David W. Wilson and Reinhard Zumkeller, Table of n, a(n) for n = 0..100 (a(n) for n = 1..55 from Reinhard Zumkeller).

Crossrefs

Cf. A004185, A193582.

Programs

Haskell

import Data.List (elemIndex)
import Data.Maybe (fromJust)
a065641 n = a065641_list !! (n-1)
a065641_list = map (fromJust . (`elemIndex` a193582_list)) [1..]
-- Reinhard Zumkeller,Aug 10 2011

Mathematica

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 *)
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 *)

Extensions

Added a(0) = 0. David W. Wilson, Jan 08 2017