A281921 10th-power analog of Keith numbers.

1, 82, 85, 94, 97, 106, 117, 459, 1197, 24615, 24657, 26184, 87664, 117099, 538168, 1049708, 1229174, 2210323, 4587773, 11019224, 96167938, 104719358, 202511251, 226456915, 821871524, 1811437987, 1832881095, 3530066559, 7414362499, 7906250753, 15607432165, 15631766564

Offset

1,2

Comments

Like Keith numbers but starting from n^10 digits to reach n.

Consider the digits of n^10. 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

Table of n, a(n) for n=1..32.

Example

106^10 = 179084769654285362176: 1 + 7 + 9 + 0 + 8 + 4 + 7 + 6 + 9 + 6 + 5 + 4 + 2 + 8 + 5 + 3 + 6 + 2 + 1 + 7 + 6 = 106.

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 *)
a281921[n_] := Join[{1}, Select[Range[10, n], keithQ[#, 10]&]]
a281921[10^6] (* Hartmut F. W. Hoft, Jun 03 2021 *)

Crossrefs

Cf. A007629, A246544, A263534.

Cf. A274769, A274770, A281915, A281916, A281917, A281918, A281919, A281920.

Sequence in context: A044982 A181468 A081648 * A303885 A305278 A025370

Adjacent sequences: A281918 A281919 A281920 * A281922 A281923 A281924

Keyword

nonn,base

Author

Paolo P. Lava, Feb 02 2017

Extensions

a(21) from Jinyuan Wang, Feb 02 2020

a(22)-a(32) from Giovanni Resta, Feb 03 2020

Status

approved