A057653 -id:A057653 - cp's OEIS frontend

A339955 Numbers that are the sum of an odd square s and an even square t such that 0 < s < t.

5, 17, 25, 37, 45, 61, 65, 73, 89, 101, 109, 113, 125, 145, 149, 153, 169, 181, 193, 197, 205, 221, 225, 245, 257, 265, 277, 281, 305, 317, 325, 333, 337, 349, 365, 373, 377, 401, 405, 409, 425, 445, 449, 481, 485, 493, 509, 521, 533, 549, 565, 569, 577, 585, 601, 605, 613

Offset: 1

Wesley Ivan Hurt, Dec 24 2020

nonn

			17 is in the sequence since 1^2 + 4^2 = 17, 1 is odd, 16 is even, and 0 < 1 < 16.

Cf. A000404, A010052, A057653, A097269.

Table[If[Sum[Mod[i, 2] Mod[n - i + 1, 2] (Floor[Sqrt[i]] - Floor[Sqrt[i - 1]]) (Floor[Sqrt[n - i]] - Floor[Sqrt[n - i - 1]]), {i, Floor[n/2]}] > 0, n, {}], {n, 700}] // Flatten

A339956 Numbers that are the sum of an even square s and an odd square t such that 0 < s < t.

Original entry on oeis.org

13, 29, 41, 53, 65, 85, 97, 117, 125, 137, 145, 157, 173, 185, 205, 221, 229, 233, 241, 261, 269, 289, 293, 305, 313, 325, 353, 365, 369, 377, 389, 397, 421, 425, 433, 445, 457, 461, 477, 485, 505, 533, 541, 545, 557, 565, 585, 593, 617, 629, 637, 641, 661, 673, 685, 689, 697

Offset: 1

Wesley Ivan Hurt, Dec 24 2020

nonn

			29 is in the sequence since 2^2 + 5^2 = 29, 4 is even, 25 is odd, and 0 < 4 < 25.

Cf. A000404, A010052, A057653, A097269.

Table[If[Sum[Mod[i + 1, 2] Mod[n - i, 2] (Floor[Sqrt[i]] - Floor[Sqrt[i - 1]]) (Floor[Sqrt[n - i]] - Floor[Sqrt[n - i - 1]]), {i, Floor[n/2]}] > 0, n, {}], {n, 700}] // Flatten

cp's OEIS Frontend

A339955 Numbers that are the sum of an odd square s and an even square t such that 0 < s < t.

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