A281919 8th-power analog of Keith numbers.

1, 30, 46, 54, 63, 207, 394, 693, 694, 718, 20196, 42664, 80051, 90135, 91447, 93136, 207846, 324121, 361401, 421609, 797607, 802702, 882227, 1531788, 1788757, 1789643, 4028916, 4176711, 6692664, 15643794, 31794346, 65335545, 140005632, 144311385, 153364253

Offset

1,2

Comments

Like Keith numbers but starting from n^8 digits to reach n.

Consider the digits of n^8. 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.

Links

Giovanni Resta, Table of n, a(n) for n = 1..40

Formula

207^8 = 3371031134626313601:

3 + 3 + 7 + 1 + 0 + 3 + 1 + 1 + 3 + 4 + 6 + 2 + 6 + 3 + 1 + 3 + 6 + 0 + 1 = 54;

3 + 7 + 1 + 0 + 3 + 1 + 1 + 3 + 4 + 6 + 2 + 6 + 3 + 1 + 3 + 6 + 0 + 1 + 54 = 105;

7 + 1 + 0 + 3 + 1 + 1 + 3 + 4 + 6 + 2 + 6 + 3 + 1 + 3 + 6 + 0 + 1 + 54 + 105 = 207.

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]<n do t:=t+1; v[t]:=add(v[k], k=t-b..t-1);
od; if v[t]=n then print(n); fi; od; end: P(10^6, 10000, 4);

Mathematica

(* function keithQ[ ] is defined in A007629 *)
a281919[n_] := Join[{1}, Select[Range[10, n], keithQ[#, 8]&]]
a281919[10^6] (* Hartmut F. W. Hoft, Jun 03 2021 *)

Crossrefs

Cf. A007629, A246544, A263534.

Cf. A274769, A274770, A281915, A281916, A281917, A281918, A281920, A281921.

Sequence in context: A152569 A114944 A075290 * A004222 A207143 A004223

Adjacent sequences: A281916 A281917 A281918 * A281920 A281921 A281922

Keyword

nonn,base

Author

Paolo P. Lava, Feb 02 2017

Extensions

a(32) from Jinyuan Wang, Feb 01 2020

Terms a(33) and beyond from Giovanni Resta, Feb 03 2020

Status

approved