A309898 For each b = 1, 2, 3, ... numbers k = 1, 2, 3, ... are inserted into the blanks within the sequence along with k * b blanks, skipping existing terms in the sequence.

1, 1, 2, 1, 1, 3, 2, 1, 1, 4, 2, 1, 3, 1, 5, 2, 1, 1, 2, 3, 6, 4, 1, 1, 2, 1, 1, 7, 3, 2, 1, 5, 1, 4, 2, 8, 1, 3, 1, 2, 1, 1, 2, 6, 9, 3, 4, 1, 1, 5, 2, 1, 1, 3, 10, 2, 1, 1, 7, 4, 2, 1, 3, 1, 2, 11, 1, 5, 6, 1, 2, 3, 4, 1, 8, 1, 2, 12, 1, 1, 3, 2, 1, 1, 4, 5, 2, 1, 3, 7, 13

Offset

1,3

Comments

b = 1 for all blanks forms A003602. b = k yields A002260.

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Example

The first 21 terms are constructed as follows:
  1 _ 2 _ _ 3 _ _ _ 4 _ _ _ _ 5 _ _ _ _ _ .
    1   _ _   2 _ _   _ _ 3 _   _ _ _ _ _ .
        1 _     _ _   2 _   _   _ _ _ _ 3 .
          1     _ _     _   _   2 _ _ _   .
                1 _     _   _     _ _ 2   .
                  1     _   _     _ _     .
                        1   _     _ _     .
                            1     _ _     .
                                  1 _     .
                                    1     .
  1 1 2 1 1 3 2 1 1 4 2 1 3 1 5 2 1 1 2 3 .

Prog

(Python)
seq = []
b = 2
for n in range(1, 100):
  seq += [n] + [-1] * n
while -1 in seq:
  i = seq.index(-1)
  seq[i] = 1
  k = 2
  blanks = b
  for s in range(i + 1, len(seq)):
    if seq[s] == -1:
      blanks -= 1
      if blanks < 0:
        seq[s] = k
        blanks = k * b
        k += 1
  b += 1
print(seq)

Crossrefs

Cf. A309898, A003602, A002260, A306470.

Sequence in context: A136622 A025474 A136575 * A193592 A243714 A343656

Adjacent sequences: A309895 A309896 A309897 * A309899 A309900 A309901

Keyword

nonn,easy

Author

Jan Koornstra, Aug 21 2019

Status

approved