rank of apparition

plural ranks of apparition

1. mathematicsGiven a positive integer m and a divisibility sequence Sₖ, the smallest index k such that Sₖ is divisible by m;

   Indeed, as shown in [18, Theorem 4.27], there exist sequences #92;#123;U#95;n#92;#125; and primes p for which p has three ranks of apparition. In the previous section, we showed that if p#61;2, then p has no more than two ranks of apparition in #92;#123;U#95;n#92;#125;.

   2013, E. L. Roettger, H. C. Williams, R. K. Guy, “Some Extensions of the Lucas Functions”, in Jonathan M. Borwein, Igor Shparlinski, Wadim Zudilin, editors, Number Theory and Related Fields, Springer, page 303

   2 more examples

   Let (W#95;n) be an EDS^([Elliptic Divisibility Sequence]) associated to an elliptic curve E#47;K and a nonzero point P#92;inE(K) of finite order. Let r#92;ge 2 be the smallest index such that W#95;r#61;0. (The number r is called the rank of apparition of the sequence.) […] Suppose that K is a finite field and that the rank of apparition r of (W#95;n) is at least 4.

   1986, Joseph H. Silverman, The Arithmetic of Elliptic Curves, Springer, page 114

   1996, D. L. Wells, Residue Counts Modulo Three for the Fibonacci Triangle, G. E. Bergum, Andreas N. Philippou, Alwyn F. Horadam (editors), Applications of Fibonacci Numbers, Kluwer Academic, Softcover reprint, page 535, A similar identification between Pascal's Triangle modulo p and the Fibonacci Triangle modulo p can be made for primes p which have the length of the period equal to twice their rank of apparition in the Fibonacci Sequence.

   Synonyms: Fibonacci entry point

2. Given a positive integer m and a divisibility sequence Sₖ, the smallest index k such that Sₖ is divisible by m; such an index for some generalisation of the concept (for example to allow multiple ranks of apparition for a given m).
   1. mathematicssuch an index for some generalisation of the concept (for example to allow multiple ranks of apparition for a given m).

      Synonyms: Fibonacci entry point