login
A377598
Positive integers D such that the generalized Pell equation X^2 - D Y^2 = -2 is solvable over the integers.
1
2, 3, 6, 11, 18, 19, 22, 27, 38, 43, 51, 54, 59, 66, 67, 83, 86, 102, 107, 114, 118, 123, 131, 134, 139, 146, 162, 163, 166, 171, 178, 179, 187, 198, 211, 214, 227, 242, 243, 246, 251, 258, 262, 267, 278, 283, 291, 307, 326, 331, 339, 347, 354, 358, 363, 374, 379, 387, 402, 411, 418, 419
OFFSET
1,1
COMMENTS
Calculated using Dario Alpern's quadratic Diophantine solver, see link.
LINKS
Eric Weisstein's World of Mathematics, Pell Equation.
EXAMPLE
The first fundamental solutions [x(n), y(n)] are (the first entry gives D(n)=a(n)):
[2, [0, 1]], [3, [1, 1]], [6, [2, 1]], [11, [3, 1]], [18, [4, 1]], [19, [13, 3]], [22, [14, 3]], [27, [5, 1]], [38, [6, 1]], [43, [59, 9]], [51, [7, 1]], [54, [22, 3]], [59, [23, 3]], [66, [8, 1]], [67, [221, 27]], [83, [9, 1]], [86, [102, 11]], [102, [10, 1]], [107, [31, 3]], [114, [32, 3]], [118, [554, 51]], [123, [11, 1]], [131, [103, 9]], [134, [382, 33]], [139, [8807, 747]], [146, [12, 1]], [162, [140, 11]], [163, [8005, 627]], [166, [41242, 3201]], [171, [13, 1]], [178, [40, 3]], [179, [2047, 153]], [187, [41, 3]], [198, [14, 1]], ...
PROG
(Python)
from itertools import count, islice
from sympy.solvers.diophantine.diophantine import diop_DN
def A377598_gen(startvalue=1): # generator of terms >= startvalue
return filter(lambda d:len(diop_DN(d, -2)), count(max(startvalue, 1)))
A377598_list = list(islice(A377598_gen(), 62)) # Chai Wah Wu, Nov 03 2024
CROSSREFS
Sequence in context: A034031 A121617 A358355 * A157656 A059100 A131512
KEYWORD
nonn
AUTHOR
Robin Visser, Nov 02 2024
STATUS
approved