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%I #25 Jun 24 2021 00:06:08
%S 1,30,46,54,63,207,394,693,694,718,20196,42664,80051,90135,91447,
%T 93136,207846,324121,361401,421609,797607,802702,882227,1531788,
%U 1788757,1789643,4028916,4176711,6692664,15643794,31794346,65335545,140005632,144311385,153364253
%N 8th-power analog of Keith numbers.
%C Like Keith numbers but starting from n^8 digits to reach n.
%C 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.
%H Giovanni Resta, <a href="/A281919/b281919.txt">Table of n, a(n) for n = 1..40</a>
%F 207^8 = 3371031134626313601:
%F 3 + 3 + 7 + 1 + 0 + 3 + 1 + 1 + 3 + 4 + 6 + 2 + 6 + 3 + 1 + 3 + 6 + 0 + 1 = 54;
%F 3 + 7 + 1 + 0 + 3 + 1 + 1 + 3 + 4 + 6 + 2 + 6 + 3 + 1 + 3 + 6 + 0 + 1 + 54 = 105;
%F 7 + 1 + 0 + 3 + 1 + 1 + 3 + 4 + 6 + 2 + 6 + 3 + 1 + 3 + 6 + 0 + 1 + 54 + 105 = 207.
%p with(numtheory): P:=proc(q, h,w) local a, b, k, t, v; global n; v:=array(1..h);
%p for n from 1 to q do b:=n^w; a:=[];
%p for k from 1 to ilog10(b)+1 do a:=[(b mod 10), op(a)]; b:=trunc(b/10); od;
%p for k from 1 to nops(a) do v[k]:=a[k]; od; b:=ilog10(n^w)+1;
%p 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);
%p od; if v[t]=n then print(n); fi; od; end: P(10^6,10000,4);
%t (* function keithQ[ ] is defined in A007629 *)
%t a281919[n_] := Join[{1}, Select[Range[10, n], keithQ[#, 8]&]]
%t a281919[10^6] (* _Hartmut F. W. Hoft_, Jun 03 2021 *)
%Y Cf. A007629, A246544, A263534.
%Y Cf. A274769, A274770, A281915, A281916, A281917, A281918, A281920, A281921.
%K nonn,base
%O 1,2
%A _Paolo P. Lava_, Feb 02 2017
%E a(32) from _Jinyuan Wang_, Feb 01 2020
%E Terms a(33) and beyond from _Giovanni Resta_, Feb 03 2020
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