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interprime n.  and  nonagonal n.

First numbers that belong to both sets:

9, 111, 154, 969, 1089, 1491, 2674, 5781, 6364, 7614, 8625, 12871, 20026, 23904, 28756, 29394, 36874, 59736, 60654, 68250, 72216, 77331, 81549, 88086, 105531, 107976, 120621, 123234, 125875, 136719, 143724, 150904, 159751, 161250, 165789, 170391, 173494, 181374, 204369, 207766, 219876, 254475, 256366, 301791, 314250, 324825, 331254, 337746, 378021, 391950, 401376, 415725, 422994, 430326, 507111, 536844, 595959, 604656, 619291, 805200, 815304, 852891, 952389, 970734, 1015476, 1042041, 1088379, 1180011, 1184079, 1204524, 1216875, 1221006, 1241766, 1288054, 1387575, 1588281, 1616700, 1654984, 1732896, 1767546, 1782501, 1812600, 1827744, 1972126, 2014386, 2035684, 2051731, 2078616, 2100250, 2193444, 2397474, 2420704, 2449899, 2485164, 2568429, 2616625, 2640891, 2646975, 2801350, 2845359, 3005334, 3024825, 3090250, 3103419, 3209779, 3256875, 3352096, 3358950, 3400221, 3525546, 3631716, 3703371, 3804864, 3900336, 3944799, 3967125, 4170894, 4239951, 4263096, 4426875, 4466325, 4545750, 4714821, 4862196, 4878711, 4903536, 5172256, 5309304, 5421975, 5439414, 5465625, 5544636, 5571099, 5615344, 6150651, 6508326, 6546564, 6565725, 6584914, 6710325, 6729724, 6856500, 6895746, 7024069, 7133574, 7223799, 7497876, 7590369, 7631659, 7923825, 7997724, 8040106, 8061339, 8114544, 8189325, 8689276, 8844375, 8989624, 9023311, 9102159, 9238125, 9443964, 9721944, 9909504, 10230075, 10254024, 10555749, 10800279, 10960725, 10997919, 11022750, 11184834, 11335500, 11423854, 11678184, 11793546, 11883664, 12313126, 12326259, 12497625, 12577116, 12884166, 13167750, 13222116, 13249341, 13413279, 13647250, 13995000, 14403871, 14432286, 14474961, 14531959, 14789836, 15079026, 15151761, 15651000, 15754789, 15784506, 15799375, 15873825, 16053219, 16218549, 16248700, 16309086, 16354449, 16475725, 16582209, 16627950, 16934500, 16996146, 17104296, 17150751, 17181756, 17243850, 17713125, 17744634, 17870950, 17997714, 18188700, 18332601, 18460989, 18477069, 18573696, 19289994, 19405200, 19537284, 19669816, 19886136, 19902825, 19952934, 19986375, 20254911, 20661075, 20678086, 21329691, 21502846, 21520200, 21728994, 21781350, 22079224, 22149606, 22520949, 22538709, 22592031, 22859586, 22895379, 23164719, 23345154, 23708124, 23781054, 23854096, 24073894, 24350059, 24423969, 24590676, 24702129, 24776571, 24888444, 24907114, 25489356, 25508250, 25659654, 26327314, 26538921, 26712684, 27198334, 27295989, 27335100, 27413406, 27668674, 27826350, 28063704, 28341891, 28461534, 28701576, 28761744, 28862164, 29225125, 29651446, 29875989.

Some larger examples :