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decagonal n.  and  Poulet n.

First numbers that belong to both sets:

1105, 1387, 2047, 3277, 6601, 13747, 16705, 19951, 31417, 74665, 83665, 88357, 90751, 275887, 390937, 514447, 604117, 642001, 741751, 748657, 769567, 916327, 1092547, 1293337, 1302451, 1433407, 1520905, 1530787, 1809697, 1907851, 2008597, 2205967, 2387797, 2746477, 2976487, 3116107, 3316951, 3375487, 3539101, 4005001, 4069297, 4101637, 4314967, 4415251, 4567837, 4863127, 5095177, 5481451, 5575501, 5766001, 6236257, 6539527, 6787327, 8095447, 8209657, 8650951, 9273547, 9371251, 9494101, 10402237, 10505701, 10635751, 11541307, 12711007, 13996951, 14026897, 15188557, 15978007, 16853077, 17116837, 17316001, 18535177, 18985627, 20117467, 20261251, 21355951, 22669501, 23283037, 26886817, 27219697, 30219757, 31150351, 32095057, 33840397, 36255451, 36448387, 36981601, 37469701, 38010307, 38903287, 39353665, 40160737, 45175201, 47903701, 51283501, 51340807, 51627817, 52204237, 53542147, 55729957, 56810137, 57172501, 58449847, 60112885, 65565457, 66932851, 68512867, 69176647, 69776785, 72543547, 80375707, 85400701, 86438857, 87558127, 92645437, 94502701, 99945007, 100907047, 109437751, 111202297, 115804501, 116321617, 117445987, 119273701, 136545067, 137763037, 139363927, 151813201, 154287451, 161423377, 166339057, 167579497, 171747577, 172272187, 177349147, 186739057, 188382487, 188821951, 195475351, 196035001, 200767645, 201789127, 202130197, 203269177, 218603617, 222524347, 226359547, 227444101, 228652201, 235476697, 238432201, 240785047, 242650717, 248290927, 249679501, 259765747, 261186001, 261703417, 267559627, 271763467, 273480637, 284166877, 284301751, 297812677, 301413001, 303639337, 305314465, 305594101, 314184487, 320454751, 323901007, 333619357, 337135501, 338458807, 339195097, 347347087, 348989101, 362569201, 364857751, 374703127, 377806687, 383425351, 390507001, 395264101, 395900557, 403095967, 404864701, 407282851, 410680357, 417027451, 421121701, 421942951, 424411501, 435358657, 437866087, 461272267, 471812701, 475468927, 478614067, 479489557, 481593997, 483351217, 490057837, 493961737, 498059647, 499310197, 507206701, 512626201, 523551601, 530714887, 549117205, 555321007, 566689927, 573183451, 582799951, 590356357, 591717787, 599135767, 600507277, 603255001, 605221501, 609361567, 615895897, 617087701, 620072251, 628868467, 629470465, 633289807, 636111451, 644004817, 659526601, 665498107, 673778827, 682528687, 692597647, 724969087, 728851507, 730364137, 738820351, 741214237, 748419127, 748638001, 751705597, 753022201, 756318751, 757639387, 764923477, 770909107, 773131927, 775135201, 779819587, 784966297, 787209277, 801866647, 829512001, 830664451, 832048447, 835051057, 843161887, 844788757, 851778817, 867022747, 867965251, 873631027, 878603701, 884304037, 892650067, 915743251, 920834197, 943795201, 967287751, 968283247, 969528337, 975765787, 990061957, 1008777001, 1011319501, 1059193297, 1070941987, 1073299501.

Some larger examples :