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A281918 7th power analog of Keith numbers.

%I A281918 #31 Jun 19 2021 16:58:02
%S A281918 1,18,27,31,34,43,53,58,68,145,187,314,826,2975,37164,40853,58530,
%T A281918 72795,77058,160703,187617,1926759,6291322,6628695,25285305,31292514,
%U A281918 33968486,54954185,71593237,125921697,555963577,575307142,2393596216,2444508547,42544333760,97812197525
%N A281918 7th power analog of Keith numbers.
%C A281918 Like Keith numbers but starting from n^7 digits to reach n.
%C A281918 Consider the digits of n^7. 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.
%C A281918 a(30) > 10^8. - _Jinyuan Wang_, Jan 30 2020
%e A281918 145^7 = 1347646586640625:
%e A281918 1 + 3 + 4 + 7 + 6 + 4 + 6 + 5 + 8 + 6 + 6 + 4 + 0 + 6 + 2 + 5 = 73;
%e A281918 3 + 4 + 7 + 6 + 4 + 6 + 5 + 8 + 6 + 6 + 4 + 0 + 6 + 2 + 5 + 73 = 145.
%p A281918 with(numtheory): P:=proc(q, h,w) local a, b, k, t, v; global n; v:=array(1..h);
%p A281918 for n from 1 to q do b:=n^w; a:=[];
%p A281918 for k from 1 to ilog10(b)+1 do a:=[(b mod 10), op(a)]; b:=trunc(b/10); od;
%p A281918 for k from 1 to nops(a) do v[k]:=a[k]; od; b:=ilog10(n^w)+1;
%p A281918 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 A281918 od; if v[t]=n then print(n); fi; od; end: P(10^6, 10000, 7);
%t A281918 (* function keithQ[ ] is defined in A007629 *)
%t A281918 a281918[n_] := Join[{1}, Select[Range[10, n], keithQ[#, 7]&]]
%t A281918 a281918[10^6] (* _Hartmut F. W. Hoft_, Jun 03 2021 *)
%Y A281918 Cf. A226971, A007629, A246544, A263534.
%Y A281918 Cf. A274769, A274770, A281915, A281916, A281917, A281919, A281920, A281921.
%K A281918 nonn,base
%O A281918 1,2
%A A281918 _Paolo P. Lava_, Feb 02 2017
%E A281918 a(28)-a(29) from _Jinyuan Wang_, Jan 30 2020
%E A281918 a(30)-a(36) from _Giovanni Resta_, Feb 03 2020