A367290 - OEIS

A367290

Lexicographically earliest sequence of distinct positive integers such that for any n > 0, a(n) and a(n+1) are congruent modulo the n-th prime number, and the least value not yet in the sequence appears as soon as possible.

1, 5, 2, 17, 3, 69, 4, 310, 6, 558, 7, 193, 8, 869, 9, 2077, 10, 1780, 11, 3562, 12, 961, 13, 6155, 14, 2439, 15, 8255, 16, 6120, 18, 12464, 19, 9472, 20, 11195, 21, 4260, 22, 24070, 23, 16133, 24, 18360, 25, 19528, 26, 27456, 27, 25905, 28, 46395, 29, 6054

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OFFSET

1,2

COMMENTS

To build the sequence:

- we start with a(1) = 1, and repeatedly:

- let a(n) be the last known term and v the least value not yet in the sequence,

- if a(n) and v are congruent modulo the n-th prime number then a(n+1) = v,

- otherwise a(n+2) = v and a(n+1) is chosen as small as possible in such a way as to satisfy the required congruences (this is always possible as two consecutive prime numbers are coprime).

This sequence is a variant of A364054, and, by design, is guaranteed to be a permutation of the positive integers (with inverse A367291).

LINKS

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

Rémy Sigrist, PARI program

Index entries for sequences that are permutations of the natural numbers

EXAMPLE

The first terms are:

n a(n) a(n) mod prime(n) a(n+1) mod prime(n)

-- ----- ----------------- -------------------

1 1 1 1

2 5 2 2

3 2 2 2