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%I #15 Aug 29 2019 15:47:25
%S 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,
%T 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,
%U 5,6,1,2,3,4,1,8,1,2,12,1,1,3,2,1,1,4,5,2,1,3,7,13
%N 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.
%C b = 1 for all blanks forms A003602. b = k yields A002260.
%H Seiichi Manyama, <a href="/A309898/b309898.txt">Table of n, a(n) for n = 1..10000</a>
%e The first 21 terms are constructed as follows:
%e 1 _ 2 _ _ 3 _ _ _ 4 _ _ _ _ 5 _ _ _ _ _ .
%e 1 _ _ 2 _ _ _ _ 3 _ _ _ _ _ _ .
%e 1 _ _ _ 2 _ _ _ _ _ _ 3 .
%e 1 _ _ _ _ 2 _ _ _ .
%e 1 _ _ _ _ _ 2 .
%e 1 _ _ _ _ .
%e 1 _ _ _ .
%e 1 _ _ .
%e 1 _ .
%e 1 .
%e 1 1 2 1 1 3 2 1 1 4 2 1 3 1 5 2 1 1 2 3 .
%o (Python)
%o seq = []
%o b = 2
%o for n in range(1, 100):
%o seq += [n] + [-1] * n
%o while -1 in seq:
%o i = seq.index(-1)
%o seq[i] = 1
%o k = 2
%o blanks = b
%o for s in range(i + 1, len(seq)):
%o if seq[s] == -1:
%o blanks -= 1
%o if blanks < 0:
%o seq[s] = k
%o blanks = k * b
%o k += 1
%o b += 1
%o print(seq)
%Y Cf. A309898, A003602, A002260, A306470.
%K nonn,easy
%O 1,3
%A _Jan Koornstra_, Aug 21 2019
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