A282757 2*n analog to Keith numbers.

5, 9, 10, 15, 19, 20, 25, 28, 30, 35, 40, 45, 47, 66, 88, 132, 198, 2006, 2740, 4012, 4419, 13635, 56357, 338540, 354164, 419966, 441972, 685704, 803678, 1528803, 1844810, 9127005, 12305952, 14315686, 14650155, 15828353, 17838087, 22618003, 37826729, 71644613

Offset

1,1

Comments

Like Keith numbers but starting from 2*n digits to reach n.

Consider the digits of 2*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..40.

Example

2*28 = 56 :
5 + 6 = 11;
6 + 11 = 17;
11 + 17 = 28.

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, 2);

Mathematica

Select[Range[10^6], Function[n, Module[{d = IntegerDigits[2 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. A282758 - A282765.

Sequence in context: A272902 A235033 A327593 * A199718 A155470 A266399

Adjacent sequences: A282754 A282755 A282756 * A282758 A282759 A282760

Keyword

nonn,base

Author

Paolo P. Lava, Feb 22 2017

Status

approved