Search a number
balanced n.  and  pentagonal n.

First numbers that belong to both sets:

12, 35, 210, 532, 590, 651, 782, 852, 2262, 2501, 2882, 3432, 3876, 7957, 8855, 10542, 10795, 11051, 11310, 11572, 11837, 12650, 13490, 13776, 16485, 16801, 31032, 35037, 37842, 38801, 40262, 40755, 45327, 45850, 51801, 54626, 55200, 56357, 57526, 144926, 150575, 159251, 173230, 174251, 176302, 177332, 181482, 190995, 193142, 201850, 202952, 204057, 205165, 207390, 214137, 215272, 219842, 220992, 222145, 230300, 232657, 235026, 239800, 247051, 251945, 258130, 278426, 288862, 290180, 299490, 306230, 322712, 332526, 367290, 368776, 397580, 405340, 416330, 437130, 461760, 497376, 550551, 552370, 570725, 572577, 578151, 581882, 589380, 619852, 629532, 631477, 635376, 637330, 639287, 667000, 671007, 681077, 683100, 703495, 713805, 715876, 722107, 730457, 738855, 740962, 762197, 777240, 779401, 796797, 814385, 832165, 838882, 861467, 870585, 882050, 884352, 891276, 893590, 907537, 926301, 928660, 957202, 988610, 1005732, 2109301, 2152207, 2177435, 2202810, 2210087, 2221025, 2287220, 2298347, 2328151, 2331890, 2403501, 2411102, 2433977, 2464645, 2507127, 2511007, 2542155, 2549972, 2557801, 2561720, 2581360, 2593180, 2648697, 2660670, 2664667, 2676676, 2692730, 2696751, 2720940, 2724982, 2790062, 2794155, 2802350, 2806452, 2822890, 2864195, 2884960, 2901626, 2909977, 2939300, 2943501, 2998387, 3053780, 3083817, 3105362, 3166087, 3183545, 3192292, 3218605, 3249440, 3262700, 3302642, 3342827, 3365257, 3369752, 3387762, 3414867, 3446626, 3451175, 3464840, 3469401, 3510585, 3533570, 3538176, 3584401, 3589040, 3616937, 3626260, 3649620, 3701276, 3715427, 3724876, 3729605, 3762792, 3815240, 3868051, 3872870, 3916376, 3935790, 3945515, 3955252, 3969880, 4004117, 4033580, 4147522, 4157505, 4247892, 4308690, 4416126, 4619160, 4778445, 4848307, 4886135, 4934987, 4973151, 5138376, 5238807, 5266877, 5351537, 5408352, 5425455, 5476926, 5696927, 5702775, 5844027, 6029035, 6438740, 6469855, 6501045, 6753265, 6772375, 6778751, 7036251, 7114437, 7173360, 7232526, 7258900, 7311792, 7558915, 7735026, 7748657, 7878750, 7913165, 7961472, 7996067, 8065482, 8079401, 8149176, 8163167, 8198197, 8254401, 8360301, 8388655, 8409952, 8502551, 8516842, 8646001, 8703717, 8739887, 8747130, 8812452, 8841562, 8848847, 8856135, 8863426, 8929180, 9002525, 9009876, 9017230, 9054045, 9120501, 9231801, 9246692, 9276510, 9313850, 9328807.

Some larger examples :