A377362 a(1) = 1; for n >= 2, a(n) = smallest m not in {a(1),...,a(n-1)} such that gcd(a(n-1)*m+1, a(k)) = 1 for all k = 1..n-1.

1, 2, 3, 4, 6, 5, 8, 9, 10, 7, 16, 12, 13, 24, 14, 15, 18, 11, 30, 19, 22, 21, 20, 23, 26, 17, 36, 28, 25, 42, 31, 46, 43, 40, 33, 34, 27, 44, 29, 32, 38, 39, 48, 35, 56, 41, 62, 45, 50, 47, 54, 37, 60, 51, 68, 57, 58, 49, 52, 55, 66, 53, 74, 63, 76, 61, 70, 64, 67, 78, 59, 80

Offset

1,2

Comments

At the Brazilian 25th Olympic Revenge it was asked to prove that this sequence is a permutation of positive integers, but the proposed solution was flawed. The question remains open.

Links

Max Alekseyev, Table of n, a(n) for n = 1..10000

ArtOfProblemSolving, How to solve this?, 2022.

Jack, Permutation of positive integers. MathOverflow, 2024.

Crossrefs

Sequence in context: A232559 A094138 A116538 * A084287 A263265 A263267

Adjacent sequences: A377359 A377360 A377361 * A377363 A377364 A377365

Keyword

nonn

Author

Max Alekseyev, Oct 26 2024

Status

approved