A366863 Minimal values of a corresponding to the numbers c listed in A366862, i.e., such that there exist integers a > b > c such that ab+c, ac+b and bc+a are perfect squares.

9, 28, 52, 57, 73, 89, 124, 129, 129, 168, 172, 177, 192, 201, 228, 289, 289, 292, 313, 339, 345, 364, 393, 408, 409, 432, 444, 456, 480, 504, 513, 513, 520, 568, 577, 577, 577, 579, 616, 628, 649, 649, 696, 705, 724, 744, 753, 784, 801, 844, 883, 889, 921, 952, 964, 969, 969, 984

Offset

1,1

Links

Table of n, a(n) for n=1..58.

Example

a(1) = 9 since (a, b, c) = (9, 7, 1) is the smallest solution with c = A366862(1) = 1: 9*7 + 1 = 64, 9*1 + 7 = 16 = 7*1 + 9 are squares.
a(2) = 28 is in the sequence since (a, b, c) = (28, 9, 4) is the smallest solution with c = A366862(2) = 4.
a(3) = 52 is in the sequence since (a, b, c) = (52, 16, 9) is the smallest solution with c = A366862(3) = 9.
a(4) = 16 is in the sequence since (a, b, c) = (57, 49, 16) is the smallest solution with c = A366862(4) = 16.
a(5) = 12 is in the sequence since (a, b, c) = (73, 24, 12) is the smallest solution with c = A366862(5) = 12.

Prog

(PARI) S=[]; for(a=1, oo, for(b=2, a-1, for(c=1, b-1, issquare(a*b+c)&& issquare(a*c+b)&& issquare(b*c+a)&& (S=setunion(S, [c])) &&print1(a", "))))

Crossrefs

Cf. A366862, A366861 (possible a-values listed in increasing order).

Sequence in context: A015245 A031308 A063155 * A135705 A321559 A041359

Adjacent sequences: A366860 A366861 A366862 * A366864 A366865 A366866

Keyword

nonn

Author

M. F. Hasler, Oct 25 2023

Status

approved