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centered triangular n.  and  de Polignac n.

First numbers that belong to both sets:

1, 50509, 111385, 176989, 189571, 208135, 220609, 245431, 503731, 811441, 831421, 1184149, 1586719, 1611499, 1760959, 1856485, 1951111, 1978579, 2308261, 2743885, 2772361, 2971585, 3467881, 3481579, 3780235, 3856819, 3934171, 4130911, 4460851, 4670191, 4733929, 5053591, 5276251, 5718385, 5759461, 6117571, 6214891, 6263839, 6467779, 6924079, 7151509, 7309585, 7415929, 7664791, 7739569, 7903981, 8636401, 8963371, 9468985, 9742279, 9895789, 10387189, 10513885, 10906669, 11028349, 12308041, 13280401, 13576609, 14643751, 14869579, 15125701, 15509161, 15790171, 15975649, 16132681, 16181911, 16498759, 16738411, 16858885, 17141671, 17426809, 18834589, 18973039, 19133419, 19564399, 19967329, 20044021, 20263951, 20897335, 21110629, 21291085, 21392929, 21563209, 21654301, 21665701, 21711331, 22170271, 22216429, 22447939, 22634011, 23563999, 23611585, 23802409, 24294901, 24829039, 25061485, 25073749, 25517251, 26202331, 26554585, 26617735, 27023671, 27163921, 27266149, 27484021, 27987121, 28246891, 29258209, 29470585, 30273835, 30815335, 31128871, 31238299, 31293085, 31526461, 32023531, 32120635, 32524489, 32916811, 33694291, 34452085, 34783561, 34913701, 34957135, 35015089, 35890159, 35904835, 36140059, 37028989, 37989085, 39375379, 40070089, 40380799, 40489831, 40677085, 41635639, 41873059, 42127051, 42318049, 42781411, 43344001, 43489261, 43991461, 44056471, 44971651, 45185449, 45449281, 45780151, 46245385, 47300761, 48180835, 48726451, 49567879, 49619629, 49757761, 49913389, 50121271, 50939635, 51852781, 53577829, 54658999, 55440481, 55458721, 56117359, 56853739, 56983099, 57057085, 57818209, 58397041, 58415761, 61200235, 61353631, 61430401, 61680235, 61757209, 62374729, 63306769, 63853651, 64245721, 65191585, 65250931, 65667109, 66224071, 67244581, 67425481, 67909069, 69697009, 69860701, 70270771, 70846885, 70908751, 71011921, 71156485, 71177149, 71591059, 72505885, 72735499, 73994329, 75030385, 75094051, 75860149, 77059585, 77490235, 77749201, 78702439, 79486681, 79595911, 80274811, 80450479, 80736349, 81353791, 82239931, 82417735, 83847079, 84296269, 84656485, 84927151, 85379221, 85809799, 85923289, 86651401, 86925235, 87474199, 87818179, 88462081, 90035635, 92846335, 93224359, 95054341, 95341135, 95988001, 96661135, 96853891, 98816359, 98913781, 99866161.