A282763 8*n analog to Keith numbers.

9, 20, 176, 184, 277, 2669, 15705, 233202, 241202, 445657, 742714, 2095479, 4697536, 10508788, 20308656, 55683878, 86603874

Offset

1,1

Comments

Like Keith numbers but starting from 8*n digits to reach n.

Consider the digits of 8*n. 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 themselves.

Links

Table of n, a(n) for n=1..17.

Example

8*20 = 160:
1 + 6 + 0 = 7;
6 + 0 + 7 = 13;
0 + 7 + 13 = 20.

Maple

with(numtheory): P:=proc(q, h, w) local a, b, k, n, t, v; v:=array(1..h);
for n from 1 to q do a:=w*n; b:=ilog10(a)+1; if b>1 then
for k from 1 to b do v[b-k+1]:=(a mod 10); a:=trunc(a/10); 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; fi; od; end: P(10^6, 1000, 8);

Mathematica

Select[Range[10^6], Function[n, Module[{d = IntegerDigits[8 n], s, k = 0}, s = Total@ d; While[s < n, AppendTo[d, s]; k++; s = 2 s - d[[k]]]; s == n]]] (* Michael De Vlieger, Feb 22 2017, after T. D. Noe at A007629 *)

Crossrefs

Cf. A282757 - A282762, A282764, A282765.

Sequence in context: A146388 A230833 A321723 * A013338 A008847 A143243

Adjacent sequences: A282760 A282761 A282762 * A282764 A282765 A282766

Keyword

nonn,base

Author

Paolo P. Lava, Feb 22 2017

Status

approved