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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.)