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decagonal n.  and  Duffinian n.

First numbers that belong to both sets:

27, 85, 175, 451, 1105, 1387, 2047, 2425, 3277, 3751, 4795, 7267, 8695, 9457, 11077, 11935, 13747, 14701, 16705, 17755, 19951, 21097, 23485, 24727, 28645, 31417, 40501, 42127, 45475, 47197, 50737, 52555, 58201, 62125, 64135, 66177, 68251, 81367, 88357, 90751, 95635, 98125, 103201, 105787, 113737, 119197, 127627, 133407, 136345, 145351, 148417, 154645, 157807, 164227, 177451, 184255, 187705, 191187, 194701, 205435, 209077, 216457, 220195, 227767, 231601, 239365, 255277, 263425, 267547, 275887, 280105, 288637, 292951, 301675, 306085, 315001, 319507, 333217, 337851, 356707, 361501, 371185, 385951, 390937, 401005, 406087, 416347, 421525, 437251, 447895, 464101, 480595, 497377, 514447, 531805, 537655, 549451, 555397, 573427, 585607, 604117, 629245, 642001, 648427, 667897, 687655, 707701, 721225, 741751, 769567, 783667, 805057, 812251, 819477, 834025, 856087, 870955, 878437, 916327, 924001, 955017, 962851, 970717, 986545, 994507, 1018585, 1034797, 1059355, 1084201, 1092547, 1109335, 1117777, 1134757, 1143295, 1160467, 1169101, 1177767, 1212751, 1221577, 1266187, 1275205, 1293337, 1302451, 1320775, 1329985, 1357807, 1404817, 1414315, 1433407, 1462285, 1471975, 1491451, 1501237, 1530787, 1550647, 1580677, 1590751, 1641601, 1672495, 1682857, 1693251, 1703677, 1714135, 1735147, 1745701, 1798951, 1809697, 1831285, 1863907, 1896817, 1907851, 1941145, 1963501, 1997275, 2008597, 2031337, 2042755, 2065687, 2077201, 2135251, 2146957, 2182267, 2205967, 2253751, 2277835, 2289925, 2314201, 2326387, 2387797, 2425027, 2437501, 2462545, 2475115, 2500351, 2513017, 2551207, 2576827, 2589685, 2615497, 2654455, 2693701, 2706847, 2733235, 2746477, 2773057, 2786395, 2826601, 2935225, 2948947, 2976487, 2990305, 3018037, 3031951, 3073885, 3116107, 3158617, 3187117, 3230107, 3244501, 3273385, 3316951, 3331537, 3360805, 3375487, 3390201, 3419725, 3449377, 3524067, 3539101, 3554167, 3584395, 3599557, 3629977, 3645235, 3675847, 3691201, 3737455, 3768451, 3815185, 3862207, 3877945, 3909517, 3925351, 3973045, 4021027, 4069297, 4101637, 4150387, 4199425, 4232277, 4248751, 4265257, 4314967, 4348267, 4415251, 4448935, 4465825, 4499701, 4550755, 4567837, 4602097, 4619275, 4671001, 4705645, 4775317, 4810345, 4827907, 4845501, 4863127, 4916197, 4933951, 4969555, 5023201, 5041147, 5077135, 5095177, 5131357, 5204101, 5258995, 5295751.

Some larger examples :