cp's OEIS Frontend

A282768 n/5 analog of Keith numbers.

%I A282768 #14 Mar 07 2017 20:58:34
%S A282768 55,110,165,220,275,330,385,440,495,530,47270,119710,685385,21526000,
%T A282768 6055017240
%N A282768 n/5 analog of Keith numbers.
%C A282768 Like Keith numbers but starting from n/5 digits to reach n.
%C A282768 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 A282768 If it exists, a(16) > 10^12. - _Lars Blomberg_ Mar 07 2017
%e A282768 530/5 = 106:
%e A282768    1 +   0 +   6 =   7;
%e A282768    0 +   6 +   7 =  13;
%e A282768    6 +   7 +  13 =  26;
%e A282768    7 +  13 +  26 =  46;
%e A282768   13 +  26 +  46 =  85;
%e A282768   26 +  46 +  85 = 157;
%e A282768   46 +  85 + 157 = 288;
%e A282768   85 + 157 + 288 = 530.
%p A282768 with(numtheory): P:=proc(q,h,w) local a, b, k, n, t, v; v:=array(1..h);
%p A282768 for n from 1/w by 1/w to q do a:=w*n; b:=ilog10(a)+1; if b>1 then
%p A282768 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 A282768 while v[t]<n do t:=t+1; v[t]:=add(v[k], k=t-b..t-1); od;
%p A282768 if v[t]=n then print(n); fi; fi; od; end: P(10^6, 1000,1/5);
%t A282768 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 A282768 Cf. A282757 - A282765, A282766, A282767, A282769.
%K A282768 nonn,base,more
%O A282768 1,1
%A A282768 _Paolo P. Lava_, Feb 27 2017
%E A282768 a(15) from _Lars Blomberg_, Mar 07 2017