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Poulet n.  and  triangular n.

First numbers that belong to both sets:

561, 2701, 4371, 8911, 10585, 18721, 33153, 41041, 49141, 93961, 104653, 115921, 157641, 226801, 289941, 314821, 334153, 534061, 665281, 721801, 831405, 873181, 915981, 1004653, 1373653, 1537381, 1755001, 1815465, 1987021, 2035153, 2233441, 2284453, 3059101, 3363121, 4014361, 4082653, 4504501, 5176153, 5489641, 5977153, 6313681, 8134561, 8231653, 8725753, 9131401, 9863461, 10185841, 10403641, 10958221, 13073941, 13694761, 14892153, 14913991, 15913261, 16666651, 18443701, 18736381, 19328653, 20081953, 20234341, 21474181, 21789901, 24904153, 27331921, 27509653, 27986421, 28406953, 30058381, 30996001, 32914441, 34890481, 35967921, 36307981, 37962541, 38171953, 42702661, 42998901, 46094401, 47253781, 48191653, 57561085, 60957361, 61754941, 62289541, 66096253, 67902031, 72884701, 74927161, 77295961, 77594653, 78795181, 79398901, 80918281, 82452061, 90014653, 93591721, 96904081, 106485121, 108596953, 113605201, 114329881, 116151661, 117251641, 117987841, 126619741, 128536561, 134767153, 135556345, 137009181, 138336661, 138736153, 139536865, 143168581, 145206361, 148910653, 150988753, 159874021, 163759753, 165938653, 167692141, 170782921, 172116181, 176597821, 188519653, 188985961, 191326141, 196049701, 207132481, 210565981, 213035761, 217517653, 220531501, 224073865, 224582221, 227132641, 232794253, 234870301, 238001653, 245388781, 264350521, 289766701, 290344753, 299671921, 308550061, 313338061, 316349281, 321197185, 326695141, 327718401, 329153653, 329769721, 338455153, 351058753, 360018361, 361307521, 363245581, 366487201, 368113411, 373669453, 374325841, 376957153, 377616421, 390922741, 393611653, 400374253, 403095421, 418226581, 424963281, 434343601, 439309261, 453652381, 457274161, 464560921, 466758181, 467491753, 471168253, 471905281, 483029821, 490518181, 504142381, 507960001, 524151253, 528043753, 539019361, 558097345, 559702153, 576691741, 579139561, 579956653, 587336401, 595590841, 608917753, 630888481, 647190253, 651514753, 656723161, 663699961, 664574653, 676880821, 681303241, 694656901, 696447181, 699735345, 700932961, 703031253, 732736621, 754020361, 758687581, 759622753, 765245881, 769006153, 807115753, 841217653, 842202361, 852081121, 866008153, 874017145, 896231953, 915641821, 922845241, 932148253, 933184801, 938376181, 951941161, 962442001, 967714021, 979363153, 1027744453, 1032101461, 1034283421, 1037560681, 1050721561, 1104194521, 1105322653, 1112103541, 1121176981, 1129146481, 1138289041, 1139434453, 1145170153, 1157839381, 1161306721, 1168256953, 1184554801, 1202142061, 1210393801, 1219858921, 1221044653, 1234125721, 1268946253, 1311616153, 1312845661, 1325172421, 1327232481, 1354991653, 1356241321, 1368769681, 1385142661, 1410521941, 1419459121, 1425860101, 1436131621, 1464568381, 1469768653, 1494595801, 1497221281, 1507746241, 1515664153, 1547543161, 1563607081, 1574362441, 1590564601, 1616387653, 1628692201, 1630062253, 1635548221, 1638294661, 1650682153, 1670044321, 1690914781.

Some larger examples :