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A281920 9th-power analog of Keith numbers.

%I A281920 #25 Jun 24 2021 00:06:23
%S A281920 1,54,71,81,196,424,451,2394,9057,51737,52141,104439,227914,228088,
%T A281920 1019555,1096369,1202713,1687563,1954556,3332130,3652731,4177592,
%U A281920 31669012,79937731,81478913,148341053,168763202,182573136,342393476,773367191,1450679282,2914657310,3282344153
%N A281920 9th-power analog of Keith numbers.
%C A281920 Like Keith numbers but starting from n^9 digits to reach n.
%C A281920 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.
%e A281920 196^9 = 426878854210636742656:
%e A281920 4 + 2 + 6 + 8 + 7 + 8 + 8 + 5 + 4 + 2 + 1 + 0 + 6 + 3 + 6 + 7 + 4 + 2 + 6 + 5 + 6 = 100;
%e A281920 2 + 6 + 8 + 7 + 8 + 8 + 5 + 4 + 2 + 1 + 0 + 6 + 3 + 6 + 7 + 4 + 2 + 6 + 5 + 6 + 100 = 196.
%p A281920 with(numtheory): P:=proc(q, h,w) local a, b, k, t, v; global n; v:=array(1..h);
%p A281920 for n from 1 to q do b:=n^w; a:=[];
%p A281920 for k from 1 to ilog10(b)+1 do a:=[(b mod 10), op(a)]; b:=trunc(b/10); od;
%p A281920 for k from 1 to nops(a) do v[k]:=a[k]; od; b:=ilog10(n^w)+1;
%p A281920 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 A281920 od; if v[t]=n then print(n); fi; od; end: P(10^6,10000,9);
%t A281920 (* function keithQ[ ] is defined in A007629 *)
%t A281920 a281920[n_] := Join[{1}, Select[Range[10, n], keithQ[#, 9]&]]
%t A281920 a281920[10^6] (* _Hartmut F. W. Hoft_, Jun 03 2021 *)
%Y A281920 Cf. A007629, A246544, A263534.
%Y A281920 Cf. A274769, A274770, A281915, A281916, A281917, A281918, A281919, A281921.
%K A281920 nonn,base
%O A281920 1,2
%A A281920 _Paolo P. Lava_, Feb 02 2017
%E A281920 a(24) from _Jinyuan Wang_, Feb 02 2020
%E A281920 a(25)-a(33) from _Giovanni Resta_, Feb 03 2020