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

1,3

Comments

See A293247 for the corresponding numerators, and additional comments.

Links

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

Rémy Sigrist, PARI program for A293248

Example

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.

Prog

(PARI) See Links section.

Crossrefs

Cf. A293247.

Sequence in context: A356149 A038566 A020652 * A096107 A329585 A128487

Adjacent sequences: A293245 A293246 A293247 * A293249 A293250 A293251

Keyword

nonn,frac

Author

Rémy Sigrist, Oct 03 2017

Status

approved