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A065641
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Smallest number with persistence n for the sort-and-subtract-sequence.
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4
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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
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OFFSET
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0,3
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
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PROG
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(Haskell)
import Data.List (elemIndex)
import Data.Maybe (fromJust)
a065641 n = a065641_list !! (n-1)
a065641_list = map (fromJust . (`elemIndex` a193582_list)) [1..]
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CROSSREFS
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KEYWORD
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nonn,base,nice
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AUTHOR
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Ulrich Schimke (ulrschimke(AT)aol.com), Dec 03 2001
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EXTENSIONS
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STATUS
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approved
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