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A319041
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Numbers k > 1 such that Pell(k) == -1 (mod k).
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4
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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EXAMPLE
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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).
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MATHEMATICA
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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