A274770 Cube analog to Keith numbers.

1, 8, 17, 18, 26, 27, 44, 55, 63, 80, 105, 187, 326, 776, 1095, 2196, 6338, 13031, 13131, 25562, 27223, 70825, 140791, 553076, 632489, 1402680, 1404312, 3183253, 11311424, 50783292, 51231313, 182252596, 255246098, 522599548, 1180697763, 2025114819, 2137581414

Offset: 1

Author

Paolo P. Lava, Jul 06 2016

Keywords

• nonn
• base

Comments

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

Consider the digits of the cube of a number 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

			776^3 = 467288576 :
4 + 6 + 7 + 2 + 8 + 8 + 5 + 7 + 6 = 53;
6 + 7 + 2 + 8 + 8 + 5 + 7 + 6 + 53 = 102;
7 + 2 + 8 + 8 + 5 + 7 + 6 + 53 + 102 = 198;
2 + 8 + 8 + 5 + 7 + 6 + 53 + 102 + 198 = 389;
8 + 8 + 5 + 7 + 6 + 53 + 102 + 198 + 389 = 776.
		

Crossrefs

Cf. A007629, A246544, A263534, A274769.

Programs

Maple

with(numtheory): P:=proc(q, h) local a,b,k,n,t,v; v:=array(1..h);
for n from 1 to q do b:=n^3; a:=[];
for k from 1 to ilog10(b)+1 do a:=[(b mod 10),op(a)]; b:=trunc(b/10); od;
for k from 1 to nops(a) do v[k]:=a[k]; od; b:=ilog10(n^3)+1;
t:=nops(a)+1; v[t]:=add(v[k], k=1..b); while v[t]
				

Mathematica

(* function keithQ[ ] is defined in A007629 *)
a274770[n_] := Join[{1, 8}, Select[Range[10, n], keithQ[#, 3]&]]
a274770[10^6] (* Hartmut F. W. Hoft, Jun 02 2021 *)

Extensions

a(34)-a(37) from Giovanni Resta, Jul 08 2016