A319043 - OEIS

%I #11 Sep 16 2018 16:41:21

%S 741,3827,11395,13067,27971,35459,39059,84587,92833,117739,134579,

%T 134945,155819,177497,189419,332949,382771,437579,469699,473891,

%U 548627,600059,632269,643259,656083,677379,724883,783579,828827,895299,966779,1015429,1021987

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

%C 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.

%C For the composite numbers k such that Pell(k) == 1 (mod k), see A319042.

%C 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?

%H Seiichi Manyama, <a href="/A319043/b319043.txt">Table of n, a(n) for n = 1..50</a>

%e k=741 is in the sequence: Pell(741) = 741*M - 1 == -1 (mod 741) (where M is a large integer).

%e k=6 is not in the sequence: Pell(6) = 70 = 6*12 - 2 !== -1 (mod 6).

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

%K nonn

%O 1,1

%A _Jon E. Schoenfield_, Sep 08 2018