{"paper":{"title":"Congruences for sequences analogous to Euler numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Hai-Yan Wang, Zhi-Hong Sun","submitted_at":"2013-07-28T14:56:09Z","abstract_excerpt":"For a given real number $a$ we define the sequence $\\{E_{n,a}\\}$ by $E_{0,a}=1$ and $E_{n,a}=-a\\sum_{k=1}^{[n/2]}\n  \\binom n{2k}E_{n-2k,a}$ $(n\\ge 1)$, where $[x]$ is the greatest integer not exceeding $x$. Since $E_{n,1}=E_n$ is the n-th Euler number, $E_{n,a}$ can be viewed as a natural generalization of Euler numbers. In this paper we deduce some identities and an inversion formula involving $\\{E_{n,a}\\}$, and establish congruences for $E_{2n,a}\\mod{2^{{\\rm ord}_2n+8}}$, $E_{2n,a}\\pmod{3^{{\\rm ord}_3n+5}}$ and $E_{2n,a}\\pmod{5^{{\\rm ord}_5n+4}}$ provided that $a$ is a nonzero integer, where"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.7370","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}