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centered pentagonal n.  and  congruent n.

First numbers that belong to both sets:

6, 31, 141, 181, 226, 276, 391, 526, 766, 856, 951, 1381, 1501, 1756, 2031, 2176, 2326, 2806, 3151, 3516, 3901, 4101, 4731, 4951, 5176, 5406, 6126, 6631, 7156, 7426, 7701, 7981, 8556, 9151, 9456, 9766, 10726, 11391, 12426, 12781, 13141, 13876, 14631, 15406, 16606, 17016, 17431, 19141, 19581, 20026, 20476, 21391, 21856, 22326, 23766, 24751, 25756, 26781, 27301, 28891, 29431, 29976, 30526, 31081, 31641, 32206, 32776, 33351, 34516, 35701, 36301, 37516, 38751, 39376, 40006, 41926, 42576, 43231, 45901, 46581, 47266, 47956, 49351, 50766, 51481, 52926, 53656, 54391, 57381, 58141, 59676, 61231, 62806, 65206, 66016, 66831, 68476, 70141, 70981, 74391, 75256, 76126, 78766, 80551, 82356, 83266, 84181, 85101, 88831, 90726, 93606, 94576, 95551, 99501, 100501, 101506, 102516, 104551, 106606, 109726, 110776, 111831, 116101, 117181, 118266, 119356, 121551, 123766, 127126, 128256, 129391, 131676, 133981, 135141, 139831, 141016, 142206, 145806, 148231, 150676, 153141, 154381, 156876, 159391, 161926, 165766, 168351, 173581, 174901, 176226, 177556, 180231, 182926, 184281, 187006, 188376, 189751, 195301, 196701, 199516, 202351, 203776, 205206, 209526, 212431, 215356, 218301, 219781, 225751, 227256, 228766, 233326, 236391, 239476, 242581, 244141, 250431, 252016, 253606, 258406, 261631, 268141, 269781, 273076, 276391, 279726, 284766, 286456, 288151, 294981, 296701, 300156, 301891, 303631, 305376, 307126, 312406, 314176, 315951, 319516, 323101, 324901, 332151, 333976, 335806, 337641, 339481, 341326, 345031, 348756, 352501, 354381, 361951, 363856, 365766, 371526, 373456, 375391, 383181, 385141, 389076, 393031, 397006, 403006, 405016, 407031, 415141, 417181, 421276, 423331, 425391, 427456, 429526, 435766, 437856, 439951, 444156, 448381, 450501, 459031, 461176, 463326, 467641, 469806, 474151, 478516, 482901, 485101, 493951, 498406, 505126, 507376, 509631, 518701, 520981, 525556, 530151, 532456, 534766, 541726, 544056, 546391, 555781, 558141, 562876, 567631, 572406, 579606, 582016, 584431, 589276, 594141, 596581, 606391, 608856, 611326, 618766, 623751, 628756, 633781.

Some larger examples :