A317024 -id:A317024 - cp's OEIS frontend

A317025 a(n) = lcm(A317024(n), A317024(n+1)).

1, 2, 6, 3, 4, 12, 15, 5, 7, 14, 10, 20, 28, 21, 24, 8, 9, 18, 22, 11, 13, 26, 30, 60, 36, 45, 35, 42, 66, 33, 39, 52, 44, 55, 40, 56, 63, 72, 88, 77, 70, 90, 99, 110, 130, 65, 80, 16, 17, 34, 38, 19, 23, 46, 50, 25, 27, 54, 58, 29, 31, 62, 32, 96, 48, 112, 84

Offset: 1

Rémy Sigrist, Jul 19 2018

nonn

All terms are distinct.

This sequence has similarities with A088178.

			a(7) = lcm(A317024(7), A317024(8)) = lcm(3, 5) = 15.

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program for A317025

Cf. A088178, A317024.

PARI
```
See Links section.
```

A354803 a(1) = 1; for n > 1, a(n) is the smallest positive number that is coprime to a(n-1) and the product a(n) * a(n-1) is distinct from all previous products a(i) * a(i-1), i=2..n-1.

Original entry on oeis.org

1, 1, 2, 3, 1, 4, 3, 5, 1, 7, 2, 5, 4, 7, 3, 8, 1, 9, 2, 11, 1, 13, 2, 15, 4, 9, 5, 7, 6, 11, 3, 13, 4, 11, 5, 8, 7, 9, 8, 11, 7, 10, 9, 11, 10, 13, 5, 16, 1, 17, 2, 19, 1, 23, 2, 25, 1, 27, 2, 29, 1, 31, 2, 37, 1, 32, 3, 16, 7, 12, 11, 13, 6, 17, 3, 19, 4, 17, 5, 19, 6, 23, 3, 25, 4, 23

Offset: 1

Scott R. Shannon, Jun 07 2022

This sequences uses similar a similar rule to A088177 but here all neighboring terms are coprime. In the first 1000000 terms the only fixed point is the first term while the smallest number not to have appeared is 2054. The sequence is conjectured to be a permutation of the positive integers.

See A354804 for the products of all pairs of terms.

			a(5) = 1 as a(4) = 3 and 1 is the smallest positive number that is coprime to 3 and whose product with 3, 1 * 3 = 3, has not previously appeared.

Scott R. Shannon, Image of the first 500000 terms.

Cf. A354804, A354749, A354759, A354753, A354754, A088177, A317024.

cp's OEIS Frontend

A317025 a(n) = lcm(A317024(n), A317024(n+1)).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI