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.

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

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

Name clarified, some terms and Maple code corrected 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