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

1,2

Links

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

Example

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

Prog

(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)

Crossrefs

Cf. A309898, A003602, A002260, A306470.

Sequence in context: A048206 A290740 A075765 * A181024 A214744 A014656

Adjacent sequences: A309896 A309897 A309898 * A309900 A309901 A309902

Keyword

nonn,easy

Author

Jan Koornstra, Aug 21 2019

Status

approved