A319168 Frobenius pseudoprimes == 1,4 (mod 5) with respect to Fibonacci polynomial x^2 - x - 1.

4181, 6721, 13201, 15251, 34561, 51841, 64079, 64681, 67861, 68251, 90061, 96049, 97921, 118441, 146611, 163081, 186961, 197209, 219781, 252601, 254321, 257761, 268801, 272611, 283361, 302101, 303101, 330929, 399001, 433621, 438751, 489601, 512461, 520801

Offset: 1

Author

Jianing Song, Sep 12 2018

Keywords

• nonn

Comments

Complement of A212423 with respect to A212424.

Intersection of A212424 and A047209.

Composite k == 1,4 (mod 5) such that Fibonacci(k) == 1 (mod k) and that k divides Fibonacci(k-1).

Examples

			4181 = 37*113 is composite, while Fibonacci(4180) == 0 (mod 4181), Fibonacci(4181) == 1 (mod 4181), so 4181 is a term.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (from Dana Jacobsen's site)
• Jon Grantham, Frobenius pseudoprimes, Mathematics of Computation 70 (234): 873-891, 2001. doi: 10.1090/S0025-5718-00-01197-2.
• Dana Jacobsen, Pseudoprime Statistics, Tables, and Data.
• A. Rotkiewicz, Lucas and Frobenius Pseudoprimes, Annales Mathematicae Silesiane, 17 (2003): 17-39.
• Eric Weisstein's World of Mathematics, Frobenius Pseudoprime.

Crossrefs

Cf. A047209, A093372, A094394, A094401, A212423, A212424.

Programs

PARI

for(n=2,500000,if(!isprime(n) && (n%5==1||n%5==4) && fibonacci(n-kronecker(5,n))%n==0 && (fibonacci(n)-kronecker(5,n))%n==0, print1(n, ", ")))