A282769 n/7 analog of Keith numbers.

301, 602, 1113, 4942, 478205, 23942940, 47885880, 178114489749

Offset

1,1

Comments

Like Keith numbers but starting from n/7 digits to reach n.

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.

If it exists, a(9) > 10^12. - Lars Blomberg Mar 07 2017

Links

Table of n, a(n) for n=1..8.

Example

1113/7 = 159:
    1 +   5 +   9 =   15;
    5 +   9 +  15 =   29;
    9 +  15 +  29 =   53;
   15 +  29 +  53 =   97;
   29 +  53 +  97 =  179;
   53 +  97 + 179 =  329;
   97 + 179 + 329 =  605;
  179 + 329 + 605 = 1113.

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, 1/7);

Mathematica

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 *)

Crossrefs

Cf. A282757 - A282765, A282766 - A282768.

Sequence in context: A004226 A297913 A298506 * A256101 A070192 A298326

Adjacent sequences: A282766 A282767 A282768 * A282770 A282771 A282772

Keyword

nonn,base,more

Author

Paolo P. Lava, Feb 27 2017

Extensions

a(8) from Lars Blomberg, Mar 07 2017

Status

approved