rank of apparition

Noun

rank of apparition (plural ranks of apparition)

1. Given a positive integer m and a divisibility sequence Sₖ, the smallest index k such that Sₖ is divisible by m;
   • 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...1986, Joseph H. Silverman, The Arithmetic of Elliptic Curves, Springer, page 114
   • 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.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...

   Synonyms:

   Fibonacci entry point

2. such an index for some generalisation of the concept (for example to allow multiple ranks of apparition for a given m).

   Synonyms:

   Fibonacci entry point