A274164 Smallest k > 0 such that F_{p-(k/p)} == 0 (mod p), where p = prime(n), F_i = A000045(i) and (a/b) is the Kronecker symbol.

3, 2, 5, 3, 1, 2, 3, 1, 5, 1, 1, 2, 1, 2, 5, 2, 1, 1, 2, 1, 5, 1, 2, 1, 5, 1, 3, 2, 1, 3, 3, 1, 3, 1, 1, 1, 2, 2, 5, 2, 1, 1, 1, 5, 2, 1, 1, 3, 2, 1, 3, 1, 1, 1, 3, 5, 1, 1, 2, 1, 2, 2, 2, 1, 5, 2, 1, 5, 2, 1, 3, 1, 3, 2, 1, 5, 1, 2, 1, 1, 1, 1, 1, 5, 1, 2, 1

Offset

1,1

Comments

a(n) <= 5 for all n (cf. Sun, Sun, 1992, p. 372).

Links

Table of n, a(n) for n=1..87.

Z. H. Sun and Z. W. Sun, Fibonacci numbers and Fermat's last theorem, Acta Arithmetica, Vol. 60, No. 4 (1992), 371-388.

Example

Prime(9) = 23 and Kronecker symbol (5/23) = -1. 23-(-1) = 24 and A000045(24) == 0 (mod 23). Since 5 is the smallest k such that A000045(23-(k/23)) == 0 (mod 23), a(9) = 5.

Mathematica

Table[Function[p, k = 1; While[! Divisible[Fibonacci[p - KroneckerSymbol[k, p]], p], k++]; k]@ Prime@ n, {n, 120}] (* Michael De Vlieger, Jun 23 2016 *)

Prog

(PARI) a(n) = my(k=1, p=prime(n)); while(Mod(fibonacci(p-kronecker(k, p)), p)!=0, k++); k

Crossrefs

Cf. A000045.

Sequence in context: A230820 A324549 A152178 * A103340 A106615 A361317

Adjacent sequences: A274161 A274162 A274163 * A274165 A274166 A274167

Keyword

nonn

Author

Felix Fröhlich, Jun 21 2016

Status

approved