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A263534 Consider the 10's complements mod 10 of the digits of a number k. Take their sum and repeat the process deleting the first addend and adding the previous sum. The sequence lists the numbers that after some iterations reach a sum equal to k. 9
29, 76, 157, 174, 191, 475, 713, 1129, 1961, 3286, 4424, 7812, 8973, 19978, 24317, 35845, 37041, 51712, 68022, 166838, 443275, 444247, 445219, 509439, 706317, 1189312, 1933197, 2686010, 10809303, 55558901, 58338037, 257990335, 504050156, 839186880 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Like Keith numbers but using the ten's complements of their digits.

a(35) > 10^9. - Robert Price, Apr 08 2019

LINKS

Table of n, a(n) for n=1..34.

EXAMPLE

For 29, the 10's complements of its digits are 8, 1. Then:

  8 + 1 = 9;

  1 + 9 = 10;

  9 + 10 = 19;

  10 + 19 = 29.

For 475, the 10's complements of its digits are 6, 3, 5. Then:

  6 + 3 + 5 = 14;

  3 + 5 + 14 = 22;

  5 + 14 + 22 = 41;

  14 + 22 + 41 = 77;

  22 + 41 + 77 = 140;

  41 + 77 + 140 = 258;

  77 + 140 + 258 = 475.

MAPLE

with(numtheory): P:=proc(q, h) local a, b, c, k, n, t, v; v:=array(1..h);

for n from 10 to q do b:=ilog10(n)+1; c:=n; a:=[];

for k from 1 to b do a:=[(10-c) mod 10, op(a)]; c:=trunc(c/10); od;

for k from 1 to b do v[k]:=a[k]; od; t:=b+1; v[t]:=add(v[k], k=1..b);

while v[t]<n do t:=t+1; v[t]:=add(v[k], k=t-b..t-1); od;

if v[t]=n then print(n); fi; od; end: P(10^9, 1000);

MATHEMATICA

Select[Range[10^5], Function[{m, n}, Last@ NestWhile[Append[#, Total@ Take[#, -m]] &, Flatten[{#, Total@ #}] &[IntegerDigits[n] /. d_?Positive :> 10 - d], Last@ # < n &, 1, 10^2] == n] @@ {IntegerLength@#, #} &] (* Michael De Vlieger, Mar 09 2018 *)

CROSSREFS

Cf. A007629.

Sequence in context: A142305 A184072 A071110 * A273360 A176185 A044167

Adjacent sequences:  A263531 A263532 A263533 * A263535 A263536 A263537

KEYWORD

nonn,base

AUTHOR

Paolo P. Lava, Oct 20 2015

EXTENSIONS

Clarified name, corrected some terms and Maple code by Paolo P. Lava, Mar 08 2018

a(30)-a(32) from Robert Price, Apr 05 2019

a(33)-a(34) from Robert Price, Apr 08 2019

STATUS

approved

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Last modified April 25 00:29 EDT 2019. Contains 322446 sequences. (Running on oeis4.)