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
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Nov 07 2020
STATUS
approved