

A241604


Least Fibonacci number smaller than prime(n)/2 which is a quadratic nonresidue modulo prime(n), or 0 if such a Fibonacci number does not exist.


4



0, 0, 2, 3, 2, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 2, 2, 2, 13, 5, 3, 2, 3, 5, 2, 3, 2, 2, 3, 3, 2, 3, 2, 2, 3, 2, 2, 5, 2, 2, 2, 21, 5, 2, 3, 2, 3, 2, 2, 3, 13, 13, 2, 3, 5, 2, 3, 2, 3, 2, 2, 2, 34, 5, 2, 2, 5, 2, 2, 3, 13, 3, 2, 2, 5, 2, 2, 3, 13
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OFFSET

1,3


COMMENTS

According to the conjecture in A241568, a(n) should be positive for all n > 2.


LINKS

ZhiWei Sun, Table of n, a(n) for n = 1..10000
Z.W. Sun, New observations on primitive roots modulo primes, arXiv preprint arXiv:1405.0290, 2014


EXAMPLE

a(4) = 3 since the Fibonacci number F(4) = 3 < prime(4)/2 is a quadratic nonresidue modulo prime(4) = 7, but the Fibonacci numbers F(1) = F(2) = 1 and F(3) = 2 are quadratic residues modulo prime(4) = 7.


MATHEMATICA

f[k_]:=Fibonacci[k]
Do[Do[If[f[k]>Prime[n]/2, Goto[bb]]; If[JacobiSymbol[f[k], Prime[n]]==1, Print[n, " ", Fibonacci[k]]; Goto[aa]]; Continue, {k, 1, (Prime[n]+1)/2}]; Label[bb]; Print[n, " ", 0]; Label[aa]; Continue, {n, 1, 80}]


CROSSREFS

Cf. A000040, A000045, A241568.
Sequence in context: A182006 A085239 A242872 * A282900 A126014 A317420
Adjacent sequences: A241601 A241602 A241603 * A241605 A241606 A241607


KEYWORD

nonn


AUTHOR

ZhiWei Sun, Apr 26 2014


STATUS

approved



