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A319041
Numbers k > 1 such that Pell(k) == -1 (mod k).
4
3, 5, 11, 13, 19, 29, 37, 43, 53, 59, 61, 67, 83, 101, 107, 109, 131, 139, 149, 157, 163, 173, 179, 181, 197, 211, 227, 229, 251, 269, 277, 283, 293, 307, 317, 331, 347, 349, 373, 379, 389, 397, 419, 421, 443, 461, 467, 491, 499, 509, 523, 541, 547, 557
OFFSET
1,1
COMMENTS
It appears that most of the terms of this sequence are primes. The composite terms are 741, 3827, 11395, 13067, 27971, ... (A319043).
The primes in the sequence give A003629 (primes == +-3 (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
It appears that this sequence is (A042999 \ {2}) UNION A319043. - Georg Fischer, Oct 17 2018
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..9999 (offset adapted by Georg Fischer, Jan 31 2019)
EXAMPLE
k = 3 is in the sequence since Pell(3) = 5 = 3*2 - 1 == -1 (mod 3).
k = 7 is not in the sequence: Pell(7) = 169 = 7*24 + 1 !== -1 (mod 7).
MATHEMATICA
Select[Range[800], Mod[Fibonacci[-#, 2], -#]== -1 &] (* Vincenzo Librandi, Sep 09 2018 after Alonso del Arte; {1} removed by Georg Fischer, Jan 31 2019 *)
CROSSREFS
Cf. A000129 (Pell numbers), A003629, A042999, A319040, A319042, A319043.
Sequence in context: A059350 A059644 A059646 * A003629 A175865 A001122
KEYWORD
nonn
AUTHOR
Jon E. Schoenfield, Sep 08 2018
STATUS
approved