cp's OEIS Frontend

A282769 n/7 analog of Keith numbers.

%I A282769 #14 Mar 07 2017 20:58:06
%S A282769 301,602,1113,4942,478205,23942940,47885880,178114489749
%N A282769 n/7 analog of Keith numbers.
%C A282769 Like Keith numbers but starting from n/7 digits to reach n.
%C A282769 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 iterations reach a sum equal to themselves.
%C A282769 If it exists, a(9) > 10^12. - _Lars Blomberg_ Mar 07 2017
%e A282769 1113/7 = 159:
%e A282769     1 +   5 +   9 =   15;
%e A282769     5 +   9 +  15 =   29;
%e A282769     9 +  15 +  29 =   53;
%e A282769    15 +  29 +  53 =   97;
%e A282769    29 +  53 +  97 =  179;
%e A282769    53 +  97 + 179 =  329;
%e A282769    97 + 179 + 329 =  605;
%e A282769   179 + 329 + 605 = 1113.
%p A282769 with(numtheory): P:=proc(q,h,w) local a, b, k, n, t, v; v:=array(1..h);
%p A282769 for n from 1/w by 1/w to q do a:=w*n; b:=ilog10(a)+1; if b>1 then
%p A282769 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 A282769 while v[t]<n do t:=t+1; v[t]:=add(v[k], k=t-b..t-1); od;
%p A282769 if v[t]=n then print(n); fi; fi; od; end: P(10^6, 1000,1/7);
%t A282769 With[{n = 7}, 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 A282769 Cf. A282757 - A282765, A282766 - A282768.
%K A282769 nonn,base,more
%O A282769 1,1
%A A282769 _Paolo P. Lava_, Feb 27 2017
%E A282769 a(8) from _Lars Blomberg_, Mar 07 2017