A282765 10*n analog to Keith numbers.

1, 2, 3, 4, 5, 6, 7, 8, 9, 14, 19, 28, 56, 176, 904, 3347, 4795, 5301, 9775, 10028, 16165, 16715, 35103, 49693, 111039, 191103, 370287, 439385, 845772, 1727706, 1836482, 3631676, 3767812, 4363796, 4499932, 5351605, 6940437, 20090073, 28246243, 38221997, 60220332

Offset: 1

Author

Paolo P. Lava, Feb 22 2017

Keywords

• nonn
• base

Comments

Like Keith numbers but starting from 10*n digits to reach n.

Consider the digits of 10*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.

Examples

			10*14 = 140:
1 + 4 + 0 = 5;
4 + 0 + 5 = 9;
0 + 5 + 9 = 14.
		

Crossrefs

Cf. A282757 - A282764.

Programs

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]
				

Mathematica

Select[Range[10^6], Function[n, Module[{d = IntegerDigits[10 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 *)