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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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 A278427

Adjacent sequences:  A309895 A309896 A309897 * A309899 A309900 A309901

KEYWORD

nonn,easy

AUTHOR

Jan Koornstra, Aug 21 2019

STATUS

approved

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Last modified January 24 13:24 EST 2020. Contains 331193 sequences. (Running on oeis4.)