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A319043
Composite numbers k such that Pell(k) == -1 (mod k).
4
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
OFFSET
1,1
COMMENTS
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?
LINKS
EXAMPLE
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).
CROSSREFS
Cf. A000129 (Pell numbers), A094395, A319040, A319041, A319042.
Sequence in context: A243778 A256634 A105391 * A044984 A252576 A188483
KEYWORD
nonn
AUTHOR
Jon E. Schoenfield, Sep 08 2018
STATUS
approved