A281426 Numerator of n-th term of sequence (or tree) S of all rational numbers generated by these rules: 0 is in S; if x is in S then x + 1 is in S, and if x + 1 is nonzero, then -1/(x + 1) is in S; duplicates are deleted as they occur.

0, 1, -1, 2, -1, 3, -1, 1, -2, 4, -1, 2, -3, 3, -2, 5, -1, 3, -4, 5, -3, 5, -2, 1, -3, 6, -1, 4, -5, 7, -4, 8, -3, 2, -5, 7, -2, 3, -5, 4, -3, 7, -1, 5, -6, 9, -5, 11, -4, 3, -7, 11, -3, 5, -8, 7, -5, 9, -2, 5, -7, 8, -5, 7, -3, 1, -4, 8, -1, 6, -7, 11, -6, 14

Offset

1,4

Comments

See A232890 for the corresponding denominators and additional comments.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..1000

Rémy Sigrist, PARI program for A281426

Rémy Sigrist, Scatterplot of A232890 vs A281426 for n=1..10000

Example

To generate S, the number 0 begets (1,-1), whence 1 begets 2 and -1/2, whereas -1 begets 0 and -1/2, both of which are (deleted )duplicates, so that g(3) = (2, -1/2).  The resulting concatenation of all the generations g(n) begins with 0, 1, -1, 2, -1/2, 3, -1/3, 1/2, -2, 4, -1/4, so that A232890 begins with 0, 1, -1, 2, -1, 3, -1, 1, -2, 4.

Prog

(PARI) See Links section.

Crossrefs

Cf. A232559, A232890.

Sequence in context: A265332 A107041 A336812 * A070099 A366381 A126760

Adjacent sequences: A281423 A281424 A281425 * A281427 A281428 A281429

Keyword

frac,sign

Author

Rémy Sigrist, Oct 05 2017

Status

approved