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A358060
Perfect squares that are the sum of a perfect square and a factorial number.
0
1, 25, 49, 121, 169, 289, 729, 784, 841, 961, 1296, 1681, 2401, 3969, 5041, 5184, 5329, 6561, 6889, 7744, 8464, 9801, 10816, 13689, 18496, 22201, 32761, 34969, 40401, 40804, 41616, 42436, 44944, 45796, 46656, 49729, 51984, 55696, 66049, 66564, 72361, 79524, 85264
OFFSET
1,2
COMMENTS
For any factorial k = m*n where m > n and both m and n are even, ((m-n)/2)^2 + k = ((m+n)/2)^2 will appear in this sequence.
EXAMPLE
13^2 = 7^2 + 5!.
MATHEMATICA
With[{f = Range[9]!}, q[n_] := AnyTrue[f, IntegerQ @ Sqrt[n - #] &]; Select[Range[Floor @ Sqrt[f[[-1]]]]^2, q]] (* Amiram Eldar, Oct 28 2022 *)
CROSSREFS
Sequence in context: A308177 A104777 A289829 * A131706 A110015 A110586
KEYWORD
nonn
AUTHOR
Walter Robinson, Oct 28 2022
STATUS
approved