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centered decagonal n.  and  self n.

First numbers that belong to both sets:

1, 31, 211, 80011, 100111, 197011, 387811, 469711, 497701, 586531, 649801, 678961, 746911, 854911, 892531, 896761, 974611, 1359811, 1559611, 1656001, 1869661, 1875781, 1987651, 2397781, 2467531, 2588401, 2595601, 2719531, 2726911, 2786311, 2793781, 2853901, 2929951, 2991511, 2999251, 3349711, 3357901, 3498661, 3582811, 3659401, 3736801, 3815011, 3885211, 3964951, 3973861, 4292011, 4375801, 4469851, 4545811, 4728781, 4806901, 4816711, 4895551, 5176531, 5268511, 5454901, 5538781, 5549311, 5633911, 5644531, 5729851, 5826601, 5837401, 6526531, 6537961, 6629761, 6733801, 6745411, 6838651, 6944311, 6956101, 7278211, 7387201, 7484761, 7595281, 7607611, 7706611, 7818751, 7931701, 7944301, 8172811, 8275411, 8288281, 8391601, 8508601, 8626411, 8639551, 8758261, 8864461, 9227611, 9363961, 9473761, 9598051, 9611911, 9737101, 9849061, 9863101, 10767781, 10885501, 11287531, 11559601, 11574811, 11696851, 11834911, 11973781, 11989261, 12269611, 12696211, 12824011, 12968551, 12984661, 13554811, 13719961, 13852801, 13869451, 14458501, 14475511, 14766211, 14783401, 14938561, 15094531, 15408901, 15549661, 15567301, 15708781, 15726511, 16191001, 16209001, 16516531, 16534711, 16680511, 16845301, 16863661, 17177311, 17195851, 17344531, 17681401, 18192781, 18364861, 18537751, 18730801, 18905401, 19080811, 19237411, 19592101, 19611901, 19770661, 19790551, 20493001, 20675611, 20695951, 20879461, 21248911, 21788281, 21976561, 22186711, 22376701, 22567501, 22737781, 22759111, 22951531, 23338801, 23707531, 23729311, 23903911, 23925781, 24299101, 24719761, 25099201, 25526701, 25707781, 26346601, 26553601, 26738281, 26761411, 27179461, 27366301, 27577261, 27812611, 28215001, 28238761, 28429201, 28644211, 28668151, 28884061, 29076661, 29294101, 29318311, 29536651, 29731411, 29951281, 30196531, 30838861, 30863701, 31087711, 31287511, 31739401, 31764601, 31966561, 31991851, 32194531, 32219911, 32448781, 32652901, 32678461, 32883301, 32908951, 33346531, 33579361, 33813001, 34282711, 34308901, 34518781, 34755661, 34993351, 35019811, 35258401, 35952211, 36193951, 36436501, 36463501, 36706951, 36951211, 37196281, 37414801, 37661401, 37936351, 38184661, 38433781, 38906551, 38934451, 39438361, 39663361, 39917251, 40455901, 40683781, 40940911, 41198851, 41457601, 41486401, 42238711, 42267781, 42529861, 42763501, 42792751, 43291531, 43556761, 43586281, 43822801, 43852411, 44089651, 44357311, 44387101, 44625781, 44655661, 44895061, 45195211, 45466201, 45707761, 45980281, 46253611, 46527751, 46558261, 46802701, 46833301, 47078461, 47632411, 47663281, 47910601, 47941561, 48781261, 49062781, 49313701, 49345111, 49628251, 49912201, 50196961, 50482531, 51632911, 51890311.

Some larger examples :