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

0,3

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.

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).

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A004185, A193582.

Sequence in context: A055714 A046762 A066290 * A121874 A144560 A076160

Adjacent sequences: A065638 A065639 A065640 * A065642 A065643 A065644

Keyword

nonn,base,nice

Author

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

Extensions

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

Status

approved