A282766 - OEIS

%I #14 Mar 13 2017 13:03:39

%S 50,642,1284,1926,2292,5088,29828,42922,53046,95968,512050,1043160,

%T 1723714,14819056,154860206,159251186,752516578,946218018,54728972948

%N n/2 analog of Keith numbers.

%C Like Keith numbers but starting from n/2 digits to reach n.

%C Consider the digits of n/2. 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(20) > 10^12. - _Lars Blomberg_ Mar 13 2017

%e 642/2 = 321:

%e 3 + 2 + 1 = 6;

%e 2 + 1 + 6 = 9;

%e 1 + 6 + 9 = 16;

%e 6 + 9 + 16 = 31;

%e 9 + 16 + 31 = 56;

%e 16 + 31 + 56 = 103;

%e 31 + 56 + 103 = 190;

%e 56 + 103 + 190 = 349;

%e 103 + 190 + 349 = 642.

%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, 1000,1/2);

%t With[{n = 2}, 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, A282767, A282768, A282769.

%K nonn,base,more

%O 1,1

%A _Paolo P. Lava_, Feb 27 2017

%E a(15)-a(19) from _Lars Blomberg_, Mar 13 2017