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.

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, 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, 9, 9, 10, 10, 23, 11, 24, 13, 25, 10, 10, 11, 26

Offset: 1

Author

Jan Koornstra, Aug 21 2019

Keywords

• nonn
• easy

Examples

			The first elements are:
  1 _ 2 _ _ 3 _ _ _ 4 _ _ _ _ 5 _ _ _ _ _
    2   _ _   3 _ _   _ 4 _ _   _ _ 5 _ _
        3 _     _ _   4   _ _   _ _   5 _
          4     _ _       _ _   5 _     _
                5 _       _ _     _     _
                  .
  1 2 2 3 4 3 3 5 6 4 4 4 7 8 5 5 9 5 5 10
		

Links

• Jan Koornstra, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A309898, A003602, A002260, A306470.

Programs

Python

seq = []
for n in range(1, 100): seq += [n] + n*[-1]
for n in range(2, len(seq)):
  value = n
  gaps = 0
  position = n - 1
  while position < len(seq):
    if seq[position] == -1:
      if gaps > 0: gaps -= 1
      else:
        seq[position] = value
        gaps = value
        value += 1
    position += 1
print(seq)