A366865 Largest elements of triples (a, b, c) with a > b > c > 0 such that ab+c, ac+b and bc+a are perfect squares.

9, 12, 19, 24, 28, 33, 40, 51, 52, 57, 60, 64, 72, 73, 84, 88, 89, 96, 99, 105, 108, 112, 116, 124, 129, 136, 144, 145, 148, 156, 163, 168, 169, 172, 177, 180, 184, 192, 193, 201, 204, 217, 220, 228, 231, 232, 240, 241, 243, 249, 260, 264, 268, 273, 276, 280, 288, 289, 291, 292, 295, 297, 304, 312, 313, 316, 324, 336, 337, 339, 345, 348, 352, 355, 364, 369, 372, 376, 385, 388, 393, 396, 408, 409, 420, 424, 432, 435, 441, 444, 448, 451, 456

Offset

1,1

Links

Table of n, a(n) for n=1..93.

Wendy Appleby, Find all triples..., Number Theory group on LinkedIn.com, Oct 25 2023.

Example

a(1) = 9 because {9,4,1} is the smallest 3-set {a,b,c} such that ab+c, ac+b and bc+a are squares, here: 9*7 + 1 = 64 and 9*1 + 7 = 16 = 7*1 + 9.

Prog

(PARI) is(a)=for(b=2, a-1, for(c = 1, b-1, issquare(a*b+c)&& issquare(a*c+b)&& issquare(b*c+a)&& return(1))
select(is, [1..456])

Crossrefs

Cf. A000290 (the squares), A366861 (same with c = 1), A366862 (possible c-values).

Sequence in context: A153973 A072702 A357185 * A366861 A364343 A157973

Adjacent sequences: A366862 A366863 A366864 * A366866 A366867 A366868

Keyword

nonn,easy

Author

M. F. Hasler, Oct 25 2023

Status

approved