A281917 6th power analog of Keith numbers.

1, 18, 45, 54, 64, 125, 218, 246, 935, 1125, 6021, 6866, 7887, 40210, 89330, 457625, 577655, 613385, 640118, 5200210, 6809148, 7293243, 10013591, 50980917, 216864574, 885859983, 4556794863, 4939169289, 8580755055, 8672110451, 18562634876, 18992278338, 36013476739

Offset

1,2

Comments

Like Keith numbers but starting from n^6 digits to reach n.

Consider the digits of n^6. 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

125^6 = 3814697265625:
3 + 8 + 1 + 4 + 6 + 9 + 7 + 2 + 6 + 5 + 6 + 2 + 5 = 64;
8 + 1 + 4 + 6 + 9 + 7 + 2 + 6 + 5 + 6 + 2 + 5 + 64 = 125.

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, 6);

Mathematica

(* function keithQ[ ] is defined in A007629 *)
a281917[n_] := Join[{1}, Select[Range[10, n], keithQ[#, 6]&]]
a281917[10^6] (* Hartmut F. W. Hoft, MJun 039 2021 *)

Crossrefs

Cf. A055577, A007629, A246544, A263534.

Cf. A274769, A274770, A281915, A281916, A281918, A281919, A281920, A281921.

Sequence in context: A177724 A095739 A055577 * A002798 A124388 A179896

Adjacent sequences: A281914 A281915 A281916 * A281918 A281919 A281920

Keyword

nonn,base

Author

Paolo P. Lava, Feb 02 2017

Extensions

a(24) from Jinyuan Wang, Jan 31 2020

a(25)-a(33) from Giovanni Resta, Jan 31 2020

Status

approved