

A053028


Odd primes p with 4 zeros in any period of the Fibonacci numbers mod p.


30



5, 13, 17, 37, 53, 61, 73, 89, 97, 109, 113, 137, 149, 157, 173, 193, 197, 233, 257, 269, 277, 293, 313, 317, 337, 353, 373, 389, 397, 421, 433, 457, 557, 577, 593, 613, 617, 653, 661, 673, 677, 701, 733, 757, 761, 773, 797, 821, 829, 853, 857, 877, 937, 953
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OFFSET

1,1


COMMENTS

Also, primes that do not divide any Lucas number.  T. D. Noe, Jul 25 2003
Although every prime divides some Fibonacci number, this is not true for the Lucas numbers. In fact, exactly 1/3 of all primes do not divide any Lucas number. See Lagarias and Moree for more details. The Lucas numbers separate the primes into three disjoint sets: (A053028) primes that do not divide any Lucas number, (A053027) primes that divide Lucas numbers of even index and (A053032) primes that divide Lucas numbers of odd index.  T. D. Noe, Jul 25 2003; revised by N. J. A. Sloane, Feb 21 2004


LINKS



FORMULA

A prime p = prime(i) is in this sequence if p > 2 and A001602(i) is odd.  T. D. Noe, Jul 25 2003


MATHEMATICA

Lucas[n_] := Fibonacci[n+1] + Fibonacci[n1]; badP={}; Do[p=Prime[n]; k=1; While[k<p&&Mod[Lucas[k], p]>0, k++ ]; If[k==p, AppendTo[badP, p]], {n, 200}]; badP


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS

Edited: Name clarified. Moree and Renault link updated. Ballot and Elia reference linked.  Wolfdieter Lang, Jan 20 2015


STATUS

approved



