OFFSET
1,1
COMMENTS
Bang proved that T(p, a) == a (mod p) for every a > 0 and every odd prime. Rayes et al. (1999) defined Chebyshev pseudoprimes to base a as composite numbers k such that T(k, a) == a (mod k).
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..1000
Thøger Bang, Congruence properties of Tchebycheff polynomials, Mathematica Scandinavica, Vol. 2, No. 2 (1955), pp. 327-333, alternative link,
David Pokrass Jacobs, Mohamed O. Rayes, and Vilmar Trevisan. Characterization of Chebyshev Numbers, Algebra and Discrete Mathematics, Vol. 2 (2008), pp. 65-82.
Mohamed O. Rayes, Vilmar Trevisan, and Paul S. Wangy, Chebyshev Polynomials and Primality Tests, ICM Technical Report, Kent State University, Kent, Ohio, 1999. See page 8.
Eric Weisstein's World of Mathematics, Chebyshev Polynomial of the First Kind.
Wikipedia, Chebyshev polynomials.
EXAMPLE
14 is in the sequence since it is composite and T(14, 3) = 26102926097 == 3 (mod 14).
MATHEMATICA
Select[Range[1000], CompositeQ[#] && Divisible[ChebyshevT[#, 3] - 3, #] &]
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Dec 05 2019
STATUS
approved