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

1,2

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.

Links

Table of n, a(n) for n=1..41.

Example

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

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, 10);

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 *)

Crossrefs

Cf. A282757 - A282764.

Sequence in context: A085153 A339111 A130010 * A033081 A032579 A151543

Adjacent sequences: A282762 A282763 A282764 * A282766 A282767 A282768

Keyword

nonn,base

Author

Paolo P. Lava, Feb 22 2017

Status

approved