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heptagonal n.  and  Lehmer n.

First numbers that belong to both sets:

3367, 4141, 9211, 19669, 25351, 81631, 92833, 144841, 196981, 371911, 401401, 442471, 521437, 530611, 577681, 670033, 677821, 730891, 950797, 1026241, 1446661, 1716859, 2212291, 2235871, 2503501, 2604571, 2812711, 3073039, 3252991, 3327559, 3604201, 3676603, 4229551, 4360621, 5481181, 5934391, 6405601, 6566671, 8655511, 9031651, 11328409, 11456491, 12328771, 12776911, 13003981, 13697191, 14169331, 14892541, 15884821, 17170171, 18778591, 19609801, 19890871, 20060473, 20401837, 20459011, 22211431, 22510501, 22887151, 25292131, 26061259, 27700609, 28235761, 28708219, 32053531, 34330531, 36494371, 39217861, 44114701, 44958841, 45383911, 47998237, 48327427, 50191681, 53377171, 54772381, 55712521, 60533221, 63018571, 67306519, 67826389, 69187411, 72379831, 74548111, 75644251, 78980671, 81244951, 82389091, 82618879, 84701371, 86456581, 89421931, 92194213, 93046351, 94885561, 96742771, 101146261, 106298821, 108264031, 110912311, 111846769, 114267661, 121128361, 122524501, 125482435, 127473991, 130057603, 133981621, 135449761, 139902181, 140201569, 145187671, 153691441, 156052651, 163244281, 168949771, 169608067, 173085121, 176429401, 186654241, 188386381, 190999591, 194511871, 197033893, 202531501, 205240711, 209796061, 215328481, 223762111, 226609321, 230433601, 233322811, 247043791, 257084491, 266292121, 275661751, 280937101, 290558731, 311403061, 317008411, 341096881, 342265951, 348141301, 356450791, 385684471, 399468241, 410925871, 416070151, 423846571, 430381921, 443602621, 451631041, 470644021, 472017091, 495665281, 505570771, 512706121, 514139191, 522779611, 534412171, 540276451, 549132871, 574617061, 576134131, 580087873, 592953901, 597583111, 603783391, 611578741, 640056001, 644865211, 651305491, 664282051, 674098471, 679033681, 693947311, 698954521, 700627591, 720860431, 729375781, 772702531, 781517881, 799298581, 802878721, 807904357, 837289051, 857540821, 859393891, 874290451, 879909661, 893091151, 902566501, 909038299, 910182781, 919748131, 950693251, 968324881, 984133441, 1002071071, 1010095351, 1026239911, 1069228381, 1094189221, 1102573501, 1108882711, 1115209921, 1125795271, 1143263485, 1166475601, 1170799741, 1172964811, 1177300951, 1192540441, 1238846911, 1258962541, 1279240171, 1286035381, 1297400731, 1311105151, 1313396221, 1327184641, 1387766461, 1409052091, 1422855337, 1437684931, 1447293211, 1473880981, 1490926471, 1495814611, 1520375311, 1571224645, 1577623921, 1580136991, 1619599843, 1633373461, 1669354441, 1687491931, 1695295141, 1724060911, 1726687981, 1731948121, 1774317241, 1779649381, 1782318451, 1830703711, 1855139341, 1860045907, 1946122651, 1960098001, 1971314281, 1985379631, 1988198701, 2047861171, 2088126151, 2105502571, 2140471411, 2152191691, 2175728251, 2187544531, 2196427741, 2274169561, 2301395191, 2350196311, 2355718477, 2377871941, 2384044081, 2393317291, 2398889857, 2421244921, 2430590131, 2432461333, 2452465621, 2458733761, 2515507021, 2601881911, 2624513401, 2630997541, 2650497961, 2660275171, 2712724291.

Some larger examples :