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arithmetic n.  and  congruent n.

First numbers that belong to both sets:

5, 6, 7, 13, 14, 15, 20, 21, 22, 23, 29, 30, 31, 37, 38, 39, 41, 45, 46, 47, 53, 54, 55, 56, 60, 61, 62, 65, 69, 70, 71, 77, 78, 79, 85, 86, 87, 92, 93, 94, 95, 96, 101, 102, 103, 109, 110, 111, 116, 118, 119, 125, 126, 127, 133, 134, 135, 137, 138, 141, 142, 143, 145, 149, 150, 151, 154, 157, 158, 159, 161, 164, 165, 166, 167, 173, 174, 181, 182, 183, 184, 188, 189, 190, 191, 197, 198, 199, 205, 206, 207, 210, 212, 213, 214, 215, 219, 220, 221, 222, 223, 224, 229, 230, 231, 237, 238, 239, 245, 246, 247, 248, 253, 254, 255, 257, 260, 261, 262, 263, 265, 269, 270, 271, 276, 277, 278, 280, 284, 285, 286, 287, 291, 293, 294, 295, 299, 301, 302, 303, 308, 309, 310, 311, 313, 317, 318, 319, 323, 326, 327, 330, 334, 335, 340, 341, 342, 343, 348, 349, 350, 351, 352, 353, 357, 358, 359, 365, 366, 367, 369, 371, 373, 374, 375, 376, 380, 381, 382, 383, 389, 390, 391, 395, 397, 398, 399, 404, 406, 407, 413, 414, 415, 421, 422, 423, 426, 429, 430, 431, 434, 437, 438, 439, 445, 446, 447, 453, 454, 455, 457, 461, 462, 463, 464, 465, 469, 470, 471, 476, 477, 478, 479, 480, 485, 486, 487, 493, 494, 495, 500, 501, 502, 503, 504, 505, 509, 510, 511, 517, 518, 519, 526, 527, 533, 534, 535, 540, 541, 542, 543, 546, 548, 550, 551, 552, 557, 558, 559, 561, 564, 565, 566, 568, 572, 573, 574, 575, 580, 581, 582, 583, 585, 589, 590, 591, 596, 597, 598, 599.

Some larger examples :