

A330207


Chebyshev pseudoprimes to base 3: composite numbers k such that T(k, 3) == 3 (mod k), where T(k, x) is the kth Chebyshev polynomial of the first kind.


3



14, 35, 119, 169, 385, 434, 574, 741, 779, 899, 935, 961, 1105, 1106, 1121, 1189, 1443, 1479, 2001, 2419, 2555, 2915, 3059, 3107, 3383, 3605, 3689, 3741, 3781, 3827, 4199, 4795, 4879, 4901, 5719, 6061, 6083, 6215, 6265, 6441, 6479, 6601, 6895, 6929, 6931, 6965
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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



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



STATUS

approved



