A281916 5th power analog of Keith numbers.

1, 28, 35, 36, 46, 51, 99, 109, 191, 239, 476, 491, 1022, 1126, 1358, 1362, 15156, 21581, 44270, 63377, 100164, 375830, 388148, 2749998, 5215505, 10158487, 81082532, 87643314, 410989134, 1485204944, 3496111364, 3829840893, 15889549579, 16107462404, 16766005098, 17608009898

Offset: 1

Author

Paolo P. Lava, Feb 02 2017

Keywords

• nonn
• base

Comments

Like Keith numbers but starting from n^5 digits to reach n.

Consider the digits of n^5. Take their sum and repeat the process deleting the first addend and adding the previous sum. The sequence lists the numbers that after some number of iterations reach a sum equal to n.

Examples

			109^5 = 15386239549:
1 + 5 + 3 + 8 + 6 + 2 + 3 + 9 + 5 + 4 + 9 = 55;
5 + 3 + 8 + 6 + 2 + 3 + 9 + 5 + 4 + 9 + 55 = 109.
		

Crossrefs

Cf. A055576, A007629, A246544, A263534.

Cf. A274769, A274770, A281915, A281917, A281918, A281919, A281920, A281921.

Programs

Maple

with(numtheory): P:=proc(q, h,w) local a, b, k, t, v; global n; v:=array(1..h);
for n from 1 to q do b:=n^w; 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^w)+1;
t:=nops(a)+1; v[t]:=add(v[k], k=1..b); while v[t]
				

Mathematica

(* function keithQ[ ] is defined in A007629 *)
a281916[n_] := Join[{1}, Select[Range[10, n], keithQ[#, 5]&]]
a281916[5*10^5] (* Hartmut F. W. Hoft, Jun 03 2021 *)

Extensions

a(27)-a(28) from Jinyuan Wang, Jan 31 2020

a(29)-a(36) from Giovanni Resta, Jan 31 2020