A338764 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) = K_n.

1, 1, 2, 3, 1, 3, 4, 5, 1, 5, 6, 7, 2, 7, 8, 9, 10, 3, 10, 11, 12, 1, 12, 3, 12, 13, 14, 15, 4, 15, 16, 17, 18, 5, 18, 19, 20, 21, 6, 1, 20, 21, 22, 23, 6, 23, 24, 25, 26, 7, 26, 2, 26, 27, 28, 7, 28, 29, 30, 31, 8, 31, 32, 33, 34, 9, 34, 35, 36, 37, 10, 37, 3

Offset

1,3

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 position of the pair substituted at n-th step.

Links

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

Rémy Sigrist, PARI program for A338764

Example

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

Prog

(PARI) See Links section.

Crossrefs

Cf. A326936, A338763.

Sequence in context: A322589 A185312 A185311 * A214582 A362502 A050375

Adjacent sequences: A338761 A338762 A338763 * A338765 A338766 A338767

Keyword

nonn

Author

Rémy Sigrist, Nov 07 2020

Status

approved