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A319043
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Composite numbers k such that Pell(k) == -1 (mod k).
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4
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741, 3827, 11395, 13067, 27971, 35459, 39059, 84587, 92833, 117739, 134579, 134945, 155819, 177497, 189419, 332949, 382771, 437579, 469699, 473891, 548627, 600059, 632269, 643259, 656083, 677379, 724883, 783579, 828827, 895299, 966779, 1015429, 1021987
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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 A319041 (Numbers k such that Pell(k) == -1 (mod k)) are primes; this sequence lists the composites.
For the composite numbers k such that Pell(k) == 1 (mod k), see A319042.
Numbers that are terms of this sequence seem to be considerably less common than those in A319042; e.g., the numbers of terms in that sequence up to 10^3, 10^4, 10^5, and 10^6 are 5, 21, 67, and 200, respectively, while the corresponding term counts here are only 1, 2, 9, and 31. Why is this?
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LINKS
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EXAMPLE
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k=741 is in the sequence: Pell(741) = 741*M - 1 == -1 (mod 741) (where M is a large integer).
k=6 is not in the sequence: Pell(6) = 70 = 6*12 - 2 !== -1 (mod 6).
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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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