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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.
0
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
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
KEYWORD
nonn
AUTHOR
M. F. Hasler, Oct 25 2023
STATUS
approved