A282758 3*n analog to Keith numbers.

7, 9, 14, 19, 21, 28, 38, 53, 54, 76, 92, 124, 1299, 18185, 20468, 31871, 32054, 37903, 128200, 152057, 175539, 193399, 214631, 303677, 1806425, 3250457, 3616693, 7870170, 10793441, 12047403, 13781464, 15035426, 18663611, 19917573, 22905596, 46531972, 101743590

Offset

1,1

Comments

Like Keith numbers but starting from 3*n digits to reach n.

Consider the digits of 3*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..37.

Example

3*28 = 84:
8 + 4 = 12;
4 + 12 = 16;
12 + 16 = 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, 3);

Mathematica

Select[Range[10^6], Function[n, Module[{d = IntegerDigits[3 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 *)

Crossrefs

Cf. A282757, A282759 - A282765.

Sequence in context: A305214 A319877 A020939 * A073457 A067873 A217460

Adjacent sequences: A282755 A282756 A282757 * A282759 A282760 A282761

Keyword

nonn,base

Author

Paolo P. Lava, Feb 22 2017

Status

approved