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octagonal n.  and  Poulet n.

First numbers that belong to both sets:

341, 645, 2465, 2821, 4033, 5461, 8321, 15841, 25761, 31621, 68101, 83333, 162401, 219781, 282133, 348161, 530881, 587861, 653333, 710533, 722261, 997633, 1053761, 1082401, 1193221, 1246785, 1333333, 1357441, 1398101, 1489665, 1584133, 1690501, 1735841, 2433601, 2487941, 2531845, 2944261, 3125281, 3186821, 3375041, 3542533, 3568661, 3581761, 3985921, 4181921, 4767841, 5044033, 5489121, 6278533, 6955541, 7232321, 8036033, 8902741, 9006401, 9533701, 10386241, 10655905, 10974881, 11205601, 12032021, 12322133, 13696033, 13747361, 13773061, 14794081, 16324001, 17870561, 21397381, 21654533, 21880801, 22369621, 22665505, 23464033, 25276421, 25520833, 25696133, 26474581, 27409541, 27664033, 31040833, 32091781, 33600533, 34124641, 36974341, 37354465, 37439201, 44482901, 45879941, 48064021, 56420033, 58679941, 63002501, 63388033, 67194401, 68621701, 69485281, 70006021, 72108421, 75681541, 79464533, 81954133, 82268033, 84164033, 89784581, 91433281, 92829781, 93030145, 93431521, 95451361, 100943201, 101152133, 102690901, 104524421, 109541461, 110413333, 111654401, 112828801, 114305441, 115196033, 116090081, 121374241, 125686241, 125841633, 129205781, 130944133, 134696801, 138828821, 139892065, 143106133, 146272901, 147028001, 149389633, 154513633, 154944533, 155203361, 157368661, 161216021, 161304001, 163954561, 167881121, 170856533, 170947105, 173401621, 176609441, 176977921, 177254533, 180497633, 185653333, 190212181, 191648161, 201261061, 206304961, 206504033, 213835861, 214038533, 220883521, 225853633, 226791685, 228988033, 230879041, 231194965, 231405701, 232460821, 238199941, 250436033, 252853921, 260736341, 263428181, 266925601, 277787141, 278943061, 291461633, 292290181, 311671361, 315351521, 319053281, 338395681, 356604421, 360145633, 368476501, 370874245, 379732501, 380137633, 388695301, 390609941, 415787041, 417767201, 418617281, 419184481, 434932961, 437247841, 449501761, 457320533, 460585861, 461329601, 464012033, 465505633, 468950021, 474970501, 488656981, 493108481, 498662561, 504870241, 509551201, 528013333, 531681281, 532800133, 536003333, 544861633, 561481921, 563947141, 573862021, 577352641, 593444545, 600893921, 602593441, 606682081, 607706401, 611812321, 615760133, 621101185, 622137601, 624732421, 638837761, 644453633, 648328801, 659846021, 689537441, 710617861, 717096641, 742550401, 746331041, 749172821, 752780161, 756205633, 759638881, 765378241, 794399041, 804978721, 811478533, 812070721, 815430533, 816024161, 840749761, 842960981, 845376533, 857100421, 863196181, 868088341, 878940833, 884701441, 887795221, 896901461, 911484421, 920711045, 944832533, 976396961, 985075681, 1005402133, 1009140161, 1021281301, 1024605121, 1064686085, 1084444481, 1090842145, 1101623381, 1152793621, 1180004001, 1183338241, 1191216133, 1192412033, 1195524181, 1198880261, 1205606533, 1217181061, 1231726981, 1234646533, 1235864033, 1249785941, 1252236421.

Some larger examples :