The Fishburn numbers, ξ( n), are defined by a formal power series expansion. ∑n=0∞ξ(n)qn=1+ ∑n=1∞∏j=1n(1-(1-q)j). For half of the primes p, there is a non-empty set of numbers T( p) lying in [0, p-1] such that if j∈ T(p), then for all n≥ 0, ξ(pn+j)≡0(mod p).
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory