A319043 Composite numbers k such that Pell(k) == -1 (mod k).

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

Author

Jon E. Schoenfield, Sep 08 2018

Keywords

• nonn

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?

Examples

			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).
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..50

Crossrefs

Cf. A000129 (Pell numbers), A094395, A319040, A319041, A319042.