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.
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
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