1,1

Also, primes that do not divide any Lucas number. - T. D. Noe (noe(AT)sspectra.com), 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 (noe(AT)sspectra.com), Jul 25 2003; revised njas, Feb 21, 2004

C. Ballot and M. Elia, Rank and period of primes in the Fibonacci sequence; a trichotomy, Fib. Quart., 45 (No. 1, 2007), 56-63 (The sequence B2).

L. C. Lagarias, The set of primes dividing the Lucas numbers has density 2/3, Pacific J. Math., 118 (1985), 449-461.

T. D. Noe, Table of n, a(n) for n=1..1000

Pieter Moree, Counting Divisors of Lucas Numbers, Pacific J. Math, Vol. 186, No. 2, 1998, pp. 267-284.

M. Renault, Fibonacci sequence modulo m

Eric Weisstein's World of Mathematics, Lucas Number

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

Lucas[n_] := Fibonacci[n+1] + Fibonacci[n-1]; 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

Cf. A001176.

Cf. A000204 (Lucas numbers), A001602 (index of the smallest Fibonacci number divisible by prime(n)), A053027, A053032.

Sequence in context: A111055 A123079 A038938 this_sequence A084165 A120130 A087484

Adjacent sequences: A053025 A053026 A053027 this_sequence A053029 A053030 A053031

nonn

Henry Bottomley (se16(AT)btinternet.com), Feb 23 2000