A282768 n/5 analog of Keith numbers.

55, 110, 165, 220, 275, 330, 385, 440, 495, 530, 47270, 119710, 685385, 21526000, 6055017240

Offset

1,1

Comments

Like Keith numbers but starting from n/5 digits to reach n.

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.

If it exists, a(16) > 10^12. - Lars Blomberg Mar 07 2017

Links

Table of n, a(n) for n=1..15.

Example

530/5 = 106:
   1 +   0 +   6 =   7;
   0 +   6 +   7 =  13;
   6 +   7 +  13 =  26;
   7 +  13 +  26 =  46;
  13 +  26 +  46 =  85;
  26 +  46 +  85 = 157;
  46 +  85 + 157 = 288;
  85 + 157 + 288 = 530.

Maple

with(numtheory): P:=proc(q, h, w) local a, b, k, n, t, v; v:=array(1..h);
for n from 1/w by 1/w to q do a:=w*n; b:=ilog10(a)+1; if b>1 then
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);
while v[t]<n do t:=t+1; v[t]:=add(v[k], k=t-b..t-1); od;
if v[t]=n then print(n); fi; fi; od; end: P(10^6, 1000, 1/5);

Mathematica

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 *)

Crossrefs

Cf. A282757 - A282765, A282766, A282767, A282769.

Sequence in context: A118151 A277273 A275124 * A217429 A154031 A044242

Adjacent sequences: A282765 A282766 A282767 * A282769 A282770 A282771

Keyword

nonn,base,more

Author

Paolo P. Lava, Feb 27 2017

Extensions

a(15) from Lars Blomberg, Mar 07 2017

Status

approved