A338763 Let L_1 = (1, 2, ...); for any n > 0, let M_n = Min_{k > 0} L_n(k) + L_n(k+1) and K_n = Min_{ k | L_n(k) + L_n(k+1) = M_n }, L_{n+1} is obtained by replacing the two terms L_n(K_n) and L_n(K_n+1) by M_n in L_n; a(n) = M_n.

3, 6, 9, 13, 15, 17, 21, 25, 28, 29, 33, 37, 38, 41, 45, 49, 53, 54, 57, 61, 65, 66, 69, 70, 73, 77, 81, 85, 86, 89, 93, 97, 101, 102, 105, 109, 113, 117, 118, 120, 121, 125, 129, 133, 134, 137, 141, 145, 149, 150, 153, 156, 157, 161, 165, 166, 169, 173, 177

Offset

1,1

Comments

In other words, we start with the natural numbers and repeatedly replace the leftmost pair of consecutive terms with minimal sum by its sum; a(n) corresponds to the sum at n-th step.

This sequence is weakly increasing, and tends to infinity (as for any m > 0, there are only finitely many runs of two or more consecutive integers with a sum < m).

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, PARI program for A338763

Formula

a(n) <= a(n+1).

Example

The first terms, alongside L_n, are:
  n   a(n)  L_n
  --  ----  ----------------------------------------------------------
   1     3  { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, ... }
   2     6  {   3,  3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, ... }
   3     9  {      6,  4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, ... }
   4    13  {      6,    9,  6, 7, 8, 9, 10, 11, 12, 13, 14, 15, ... }
   5    15  {      6,    9,   13,  8, 9, 10, 11, 12, 13, 14, 15, ... }
   6    17  {         15,     13,  8, 9, 10, 11, 12, 13, 14, 15, ... }
   7    21  {         15,     13,   17,  10, 11, 12, 13, 14, 15, ... }
   8    25  {         15,     13,   17,    21,   12, 13, 14, 15, ... }
   9    28  {         15,     13,   17,    21,     25,   14, 15, ... }
  10    29  {             28,       17,    21,     25,   14, 15, ... }

Prog

(PARI) See Links section.

Crossrefs

Cf. A326936, A338764.

Sequence in context: A061514 A078559 A317557 * A159908 A236761 A088364

Adjacent sequences: A338760 A338761 A338762 * A338764 A338765 A338766

Keyword

nonn

Author

Rémy Sigrist, Nov 07 2020

Status

approved