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%I #22 Jun 05 2021 00:05:42
%S 1,28,35,36,46,51,99,109,191,239,476,491,1022,1126,1358,1362,15156,
%T 21581,44270,63377,100164,375830,388148,2749998,5215505,10158487,
%U 81082532,87643314,410989134,1485204944,3496111364,3829840893,15889549579,16107462404,16766005098,17608009898
%N 5th power analog of Keith numbers.
%C Like Keith numbers but starting from n^5 digits to reach n.
%C Consider the digits of n^5. 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 109^5 = 15386239549:
%e 1 + 5 + 3 + 8 + 6 + 2 + 3 + 9 + 5 + 4 + 9 = 55;
%e 5 + 3 + 8 + 6 + 2 + 3 + 9 + 5 + 4 + 9 + 55 = 109.
%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(10^6,10000,5);
%t (* function keithQ[ ] is defined in A007629 *)
%t a281916[n_] := Join[{1}, Select[Range[10, n], keithQ[#, 5]&]]
%t a281916[5*10^5] (* _Hartmut F. W. Hoft_, Jun 03 2021 *)
%Y Cf. A055576, A007629, A246544, A263534.
%Y Cf. A274769, A274770, A281915, A281917, A281918, A281919, A281920, A281921.
%K nonn,base
%O 1,2
%A _Paolo P. Lava_, Feb 02 2017
%E a(27)-a(28) from _Jinyuan Wang_, Jan 31 2020
%E a(29)-a(36) from _Giovanni Resta_, Jan 31 2020
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