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 A319040 Numbers k > 1 such that Pell(k) == 1 (mod k). 3
 7, 17, 23, 31, 35, 41, 47, 71, 73, 79, 89, 97, 103, 113, 127, 137, 151, 167, 169, 191, 193, 199, 223, 233, 239, 241, 257, 263, 271, 281, 311, 313, 337, 353, 359, 367, 383, 385, 401, 409, 431, 433, 439, 449, 457, 463, 479, 487, 503, 521, 569, 577, 593, 599 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS It appears that most of the terms of this sequence are primes. The composite terms are 35, 169, 385, 899, 961, 1121, ... (A319042). The primes in the sequence give A001132 (primes == +-1 (mod 8)), since for primes p we have Pell(p) == (2/p) (mod p) where (2/p) is the Legendre symbol. - Jianing Song, Sep 10 2018 LINKS EXAMPLE k = 7 is in the sequence since Pell(7) = 169 = 7 * 24 + 1 == 1 (mod 7). k = 11 is not in the sequence: Pell(11) = 5741 = 11 * 522 - 1 !== 1 (mod 11). k = 35 is in the sequence: Pell(35) = 8822750406821 = 35 * 252078583052 + 1 == 1 (mod 35). MAPLE isA319040 := k -> simplify(2^(k-1)*hypergeom([1-k/2, (1-k)/2], [1-k], -1)) mod k = 1: A319040List := b -> select(isA319040, [\$1..b]): A319040List(600); # Peter Luschny, Sep 09 2018 MATHEMATICA Select[Range, Mod[Fibonacci[#, 2], #] == 1 &] (* Alonso del Arte, Sep 08 2018 *) CROSSREFS Cf. A000129 (Pell numbers), A001132, A023173, A319041, A319042, A319043. Sequence in context: A032454 A107643 A289363 * A216838 A198441 A058529 Adjacent sequences:  A319037 A319038 A319039 * A319041 A319042 A319043 KEYWORD nonn AUTHOR Jon E. Schoenfield, Sep 08 2018 STATUS approved

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Last modified July 13 16:22 EDT 2020. Contains 335688 sequences. (Running on oeis4.)