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%I #14 Mar 07 2017 20:58:34
%S 55,110,165,220,275,330,385,440,495,530,47270,119710,685385,21526000,
%T 6055017240
%N n/5 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 iterations reach a sum equal to themselves.
%C If it exists, a(16) > 10^12. - _Lars Blomberg_ Mar 07 2017
%e 530/5 = 106:
%e 1 + 0 + 6 = 7;
%e 0 + 6 + 7 = 13;
%e 6 + 7 + 13 = 26;
%e 7 + 13 + 26 = 46;
%e 13 + 26 + 46 = 85;
%e 26 + 46 + 85 = 157;
%e 46 + 85 + 157 = 288;
%e 85 + 157 + 288 = 530.
%p with(numtheory): P:=proc(q,h,w) local a, b, k, n, t, v; v:=array(1..h);
%p for n from 1/w by 1/w to q do a:=w*n; b:=ilog10(a)+1; if b>1 then
%p for k from 1 to b do v[b-k+1]:=(a mod 10); a:=trunc(a/10); od; t:=b+1; v[t]:=add(v[k], k=1..b);
%p while v[t]<n do t:=t+1; v[t]:=add(v[k], k=t-b..t-1); od;
%p if v[t]=n then print(n); fi; fi; od; end: P(10^6, 1000,1/5);
%t With[{n = 5}, Select[Range[10 n, 10^6, n], Function[k, Last@ NestWhile[Append[Rest@ #, Total@ #] &, IntegerDigits[k/n], Total@ # <= k &] == k]]] (* _Michael De Vlieger_, Feb 27 2017 *)
%Y Cf. A282757 - A282765, A282766, A282767, A282769.
%K nonn,base,more
%O 1,1
%A _Paolo P. Lava_, Feb 27 2017
%E a(15) from _Lars Blomberg_, Mar 07 2017
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