cp's OEIS Frontend

A282767 n/3 analog of Keith numbers.

%I A282767 #14 Mar 13 2017 13:03:47
%S A282767 45,609,1218,1827,3213,21309,28206,29319,31917,39333,47337,78666,
%T A282767 102090,117999,204180,406437,302867592,4507146801,5440407522
%N A282767 n/3 analog of Keith numbers.
%C A282767 Like Keith numbers but starting from n/3 digits to reach n.
%C A282767 Consider the digits of n/3. 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 A282767 If it exists, a(20) > 10^12. - _Lars Blomberg_ Mar 13 2017
%e A282767 609/3 = 203:
%e A282767 2 + 0 + 3 = 5;
%e A282767 0 + 3 + 5 = 8;
%e A282767 3 + 5 + 8 = 16;
%e A282767 5 + 8 + 16 = 29;
%e A282767 8 + 16 + 29 = 53;
%e A282767 16 + 29 + 53 = 98;
%e A282767 29 + 53 + 98 = 180;
%e A282767 53 + 98 + 180 = 331;
%e A282767 98 + 180 + 331 = 609.
%p A282767 with(numtheory): P:=proc(q,h,w) local a, b, k, n, t, v; v:=array(1..h);
%p A282767 for n from 1/w by 1/w to q do a:=w*n; b:=ilog10(a)+1; if b>1 then
%p A282767 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 A282767 while v[t]<n do t:=t+1; v[t]:=add(v[k], k=t-b..t-1); od;
%p A282767 if v[t]=n then print(n); fi; fi; od; end: P(10^6, 1000,1/3);
%t A282767 With[{n = 3}, 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 A282767 Cf. A282757 - A282765, A282766, A282768, A282769.
%K A282767 nonn,base,more
%O A282767 1,1
%A A282767 _Paolo P. Lava_, Feb 27 2017
%E A282767 a(17)-a(19) from _Lars Blomberg_, Mar 13 2017