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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.
0
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
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
KEYWORD
nonn
AUTHOR
Felix Fröhlich, Jun 21 2016
STATUS
approved