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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.
2
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
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
Sequence in context: A322589 A185312 A185311 * A214582 A362502 A050375
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Nov 07 2020
STATUS
approved