A281920 9th-power analog of Keith numbers.

1, 54, 71, 81, 196, 424, 451, 2394, 9057, 51737, 52141, 104439, 227914, 228088, 1019555, 1096369, 1202713, 1687563, 1954556, 3332130, 3652731, 4177592, 31669012, 79937731, 81478913, 148341053, 168763202, 182573136, 342393476, 773367191, 1450679282, 2914657310, 3282344153

Offset

1,2

Comments

Like Keith numbers but starting from n^9 digits to reach n.

Consider the digits of n^9. 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..33.

Example

196^9 = 426878854210636742656:
4 + 2 + 6 + 8 + 7 + 8 + 8 + 5 + 4 + 2 + 1 + 0 + 6 + 3 + 6 + 7 + 4 + 2 + 6 + 5 + 6 = 100;
2 + 6 + 8 + 7 + 8 + 8 + 5 + 4 + 2 + 1 + 0 + 6 + 3 + 6 + 7 + 4 + 2 + 6 + 5 + 6 + 100 = 196.

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, 9);

Mathematica

(* function keithQ[ ] is defined in A007629 *)
a281920[n_] := Join[{1}, Select[Range[10, n], keithQ[#, 9]&]]
a281920[10^6] (* Hartmut F. W. Hoft, Jun 03 2021 *)

Crossrefs

Cf. A007629, A246544, A263534.

Cf. A274769, A274770, A281915, A281916, A281917, A281918, A281919, A281921.

Sequence in context: A157934 A335035 A350886 * A005129 A039532 A007244

Adjacent sequences: A281917 A281918 A281919 * A281921 A281922 A281923

Keyword

nonn,base

Author

Paolo P. Lava, Feb 02 2017

Extensions

a(24) from Jinyuan Wang, Feb 02 2020

a(25)-a(33) from Giovanni Resta, Feb 03 2020

Status

approved