A330398 For any n > 0, let S_n(0) be the concatenation of the numbers in the range 1..n (in increasing order); for k=1..n, S_n(k) is obtained by removing the rightmost occurrence of k in S_n(k-1), if any; a(n) is the numerical value of S_n(n) (or 0 if S_n(n) is empty).

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31, 3411, 345111, 34561111, 3456711111, 345678111111, 34567891111111, 1234567891011111, 1234567891111110, 1234567891111110, 14567891111102, 14567891111022, 14567891110222, 14567891112222, 14567891122222, 14567891222222

Offset

1,13

Comments

In other words, we concatenate the first n positive numbers, and then we decimate them from the right; a(n) is what remains at the end of this procedure.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..1341

Rémy Sigrist, C# program for A330398

Example

For n = 13:
- we have:
  k   S_13(k)
  --  -----------------
   0  12345678910111213
   1   1234567891011123
   2    123456789101113
   3     12345678910111
   4      1235678910111
   5       123678910111
   6        12378910111
   7         1238910111
   8          123910111
   9           12310111
  10             123111
  11               1231
  12                 31
  13                 31
- hence a(13) = 31.

Prog

(C#) See Links section.

Crossrefs

Cf. A007908.

Sequence in context: A276111 A271070 A262926 * A218661 A183783 A072913

Adjacent sequences: A330395 A330396 A330397 * A330399 A330400 A330401

Keyword

nonn,base

Author

Rémy Sigrist, Feb 25 2020

Status

approved