cp's OEIS Frontend

A281921 10th-power analog of Keith numbers.

%I A281921 #29 Jun 08 2021 02:30:04
%S A281921 1,82,85,94,97,106,117,459,1197,24615,24657,26184,87664,117099,538168,
%T A281921 1049708,1229174,2210323,4587773,11019224,96167938,104719358,
%U A281921 202511251,226456915,821871524,1811437987,1832881095,3530066559,7414362499,7906250753,15607432165,15631766564
%N A281921 10th-power analog of Keith numbers.
%C A281921 Like Keith numbers but starting from n^10 digits to reach n.
%C A281921 Consider the digits of n^10. 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 A281921 106^10 = 179084769654285362176: 1 + 7 + 9 + 0 + 8 + 4 + 7 + 6 + 9 + 6 + 5 + 4 + 2 + 8 + 5 + 3 + 6 + 2 + 1 + 7 + 6 = 106.
%p A281921 with(numtheory): P:=proc(q, h,w) local a, b, k, t, v; global n; v:=array(1..h);
%p A281921 for n from 1 to q do b:=n^w; a:=[];
%p A281921 for k from 1 to ilog10(b)+1 do a:=[(b mod 10), op(a)]; b:=trunc(b/10); od;
%p A281921 for k from 1 to nops(a) do v[k]:=a[k]; od; b:=ilog10(n^w)+1;
%p A281921 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 A281921 od; if v[t]=n then print(n); fi; od; end: P(10^6,10000,4);
%t A281921 (* function keithQ[ ] is defined in A007629 *)
%t A281921 a281921[n_] := Join[{1}, Select[Range[10, n], keithQ[#, 10]&]]
%t A281921 a281921[10^6] (* _Hartmut F. W. Hoft_, Jun 03 2021 *)
%Y A281921 Cf. A007629, A246544, A263534.
%Y A281921 Cf. A274769, A274770, A281915, A281916, A281917, A281918, A281919, A281920.
%K A281921 nonn,base
%O A281921 1,2
%A A281921 _Paolo P. Lava_, Feb 02 2017
%E A281921 a(21) from _Jinyuan Wang_, Feb 02 2020
%E A281921 a(22)-a(32) from _Giovanni Resta_, Feb 03 2020