Regularity properties of the Stern enumeration of the rationals
| dc.creator | Reznick, Bruce | |
| dc.date | 2006-10-19 | |
| dc.date.accessioned | 2026-07-07T07:29:14Z | |
| dc.date.available | 2026-07-07T07:29:14Z | |
| dc.description | The Stern sequence (s(n)) is defined by s(0) = 0, s(1) = 1, s(2n) = s(n), s(2n+1) = s(n) + s(n+1). Stern showed in 1858 that gcd(s(n),s(n+1)) = 1, and that for every pair of relatively prime positive integers (a,b), there exists a unique n so that s(n) = a and s(n+1) = b. We show that, in a strong sense, the average value of s(n)/s(n+1) is 3/2, and that for all d, (s(n),s(n+1)) is uniformly distributed among all feasible pairs of congruence classes modulo d. More precise results are presented for d = 2 and 3. | |
| dc.description | Submitted for publication | |
| dc.identifier | https://arxiv.org/abs/math/0610601 | |
| dc.identifier | http://arxiv.org/abs/math/0610601 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/118025 | |
| dc.subject | Number Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 05A15, 11B37, 11B57, 11B75 | |
| dc.title | Regularity properties of the Stern enumeration of the rationals | |
| dc.type | text |