A293248 Let S be the sequence of rational numbers generated by these rules: 1 is in S, and if u/v is in S (with gcd(u, v) = 1), then (u+1)/v and u/(v+1) are in S, and duplicates are deleted as they occur; a(n) = the denominator of the n-th term of S.

1, 1, 2, 1, 3, 1, 2, 3, 4, 1, 5, 1, 2, 5, 6, 1, 3, 5, 7, 1, 2, 4, 5, 7, 8, 1, 3, 7, 9, 1, 2, 3, 4, 7, 8, 9, 10, 1, 5, 7, 11, 1, 2, 5, 6, 7, 8, 11, 12, 1, 3, 5, 3, 4, 9, 11, 13, 1, 2, 4, 11, 13, 14, 1, 3, 5, 11, 13, 15, 1, 2, 3, 4, 5, 6, 11, 12, 13, 14, 15, 16

Offset: 1

Author

Rémy Sigrist, Oct 03 2017

Keywords

• nonn
• frac

Comments

See A293247 for the corresponding numerators, and additional comments.

Examples

			S(1) = 1 by definition; so a(1) = 1.
(1+1)/1 = 2 has not yet occurred; so S(2) = 2 and a(2) = 1.
1/(1+1) = 1/2 has not yet occurred; so S(3) = 1/2 and a(3) = 2.
(2+1)/1 = 3 has not yet occurred; so S(4) = 3 and a(4) = 1.
2/(1+1) = 1 has already occurred.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, PARI program for A293248

Crossrefs

Cf. A293247.

Programs

PARI

See Links section.