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A309899 Numbers k = 1, 2, 3, ... are added to the sequence along with k blanks. Next, the numbers k + 1 are inserted on the blanks along with k + 1 blanks. This process is then repeated.

%I A309899 #10 Aug 29 2019 20:11:22
%S A309899 1,2,2,3,4,3,3,5,6,4,4,4,7,8,5,5,9,5,5,10,6,6,11,12,6,6,6,7,7,13,14,8,
%T A309899 7,7,15,8,7,7,16,9,17,8,8,18,9,10,8,8,8,19,20,9,9,11,10,21,22,9,9,12,
%U A309899 9,9,10,10,23,11,24,13,25,10,10,11,26
%N A309899 Numbers k = 1, 2, 3, ... are added to the sequence along with k blanks. Next, the numbers k + 1 are inserted on the blanks along with k + 1 blanks. This process is then repeated.
%H A309899 Jan Koornstra, <a href="/A309899/b309899.txt">Table of n, a(n) for n = 1..10000</a>
%e A309899 The first elements are:
%e A309899   1 _ 2 _ _ 3 _ _ _ 4 _ _ _ _ 5 _ _ _ _ _
%e A309899     2   _ _   3 _ _   _ 4 _ _   _ _ 5 _ _
%e A309899         3 _     _ _   4   _ _   _ _   5 _
%e A309899           4     _ _       _ _   5 _     _
%e A309899                 5 _       _ _     _     _
%e A309899                   .
%e A309899   1 2 2 3 4 3 3 5 6 4 4 4 7 8 5 5 9 5 5 10
%o A309899 (Python)
%o A309899 seq = []
%o A309899 for n in range(1, 100): seq += [n] + n*[-1]
%o A309899 for n in range(2, len(seq)):
%o A309899   value = n
%o A309899   gaps = 0
%o A309899   position = n - 1
%o A309899   while position < len(seq):
%o A309899     if seq[position] == -1:
%o A309899       if gaps > 0: gaps -= 1
%o A309899       else:
%o A309899         seq[position] = value
%o A309899         gaps = value
%o A309899         value += 1
%o A309899     position += 1
%o A309899 print(seq)
%Y A309899 Cf. A309898, A003602, A002260, A306470.
%K A309899 nonn,easy
%O A309899 1,2
%A A309899 _Jan Koornstra_, Aug 21 2019