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A281917 6th power analog of Keith numbers.

%I A281917 #31 Aug 03 2025 23:40:01
%S A281917 1,18,45,54,64,125,218,246,935,1125,6021,6866,7887,40210,89330,457625,
%T A281917 577655,613385,640118,5200210,6809148,7293243,10013591,50980917,
%U A281917 216864574,885859983,4556794863,4939169289,8580755055,8672110451,18562634876,18992278338,36013476739
%N A281917 6th power analog of Keith numbers.
%C A281917 Like Keith numbers but starting from n^6 digits to reach n.
%C A281917 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.
%e A281917 125^6 = 3814697265625:
%e A281917 3 + 8 + 1 + 4 + 6 + 9 + 7 + 2 + 6 + 5 + 6 + 2 + 5 = 64;
%e A281917 8 + 1 + 4 + 6 + 9 + 7 + 2 + 6 + 5 + 6 + 2 + 5 + 64 = 125.
%p A281917 with(numtheory): P:=proc(q, h,w) local a, b, k, t, v; global n; v:=array(1..h);
%p A281917 for n from 1 to q do b:=n^w; a:=[];
%p A281917 for k from 1 to ilog10(b)+1 do a:=[(b mod 10), op(a)]; b:=trunc(b/10); od;
%p A281917 for k from 1 to nops(a) do v[k]:=a[k]; od; b:=ilog10(n^w)+1;
%p A281917 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 A281917 od; if v[t]=n then print(n); fi; od; end: P(10^6,10000,6);
%t A281917 (* function keithQ[n_, e_] is defined in A007629 *)
%t A281917 a281917[n_] := Join[{1}, Select[Range[10, n], keithQ[#, 6]&]]
%t A281917 a281917[10^4] (* _Hartmut F. W. Hoft_, Jun 03 2021 *)
%Y A281917 Cf. A055577, A007629, A246544, A263534.
%Y A281917 Cf. A274769, A274770, A281915, A281916, A281918, A281919, A281920, A281921.
%K A281917 nonn,base
%O A281917 1,2
%A A281917 _Paolo P. Lava_, Feb 02 2017
%E A281917 a(24) from _Jinyuan Wang_, Jan 31 2020
%E A281917 a(25)-a(33) from _Giovanni Resta_, Jan 31 2020