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de Polignac n.  and  octagonal n.

First numbers that belong to both sets:

1, 1541, 2465, 14981, 18565, 30401, 64533, 89441, 125665, 300833, 312341, 324065, 439301, 481601, 653333, 922965, 1011521, 1193221, 1262305, 1357441, 1549445, 1628033, 1654661, 1735841, 1818965, 1875461, 1932821, 2050133, 2305633, 2358533, 2390561, 2487941, 2826581, 2932385, 3581761, 3740833, 3767681, 4013633, 4139525, 4153633, 4935701, 5075201, 5312021, 5408261, 6071941, 6313301, 6738005, 7028821, 7195105, 7250965, 7686401, 8393441, 8534533, 8697221, 8758625, 9215521, 9342145, 9384545, 9792133, 9835541, 10054021, 10120033, 10792033, 10974881, 11136133, 11205601, 11321861, 11840533, 12200833, 12395201, 12566533, 13440833, 13517141, 13901921, 14057345, 14555221, 14714245, 14874133, 17637025, 18046721, 18135125, 18342241, 18490901, 19212821, 19425985, 20134661, 20165761, 20635141, 20792801, 21493633, 21751361, 22238741, 22468033, 22797633, 23263105, 23464033, 23531201, 23564821, 24038021, 24242261, 25590881, 27337045, 27518465, 27956321, 28213333, 28842401, 29328133, 29403221, 29516033, 29629061, 30121345, 30197441, 30464533, 32406533, 32524961, 32921281, 34003333, 34084181, 34246165, 34327301, 34530561, 36470533, 36554261, 36680033, 36806021, 36848065, 36932225, 37185281, 37651461, 38334725, 38721761, 39154081, 39763361, 40025921, 41084801, 44482901, 44621633, 45458561, 45786133, 46586561, 46823301, 47013125, 48208225, 48738821, 49369633, 49662145, 51534785, 51684101, 52484101, 53949761, 55075105, 55280961, 55538821, 55797281, 56264021, 57360641, 57465633, 59318533, 59692641, 60606085, 60930133, 61038341, 61689605, 61744033, 61852961, 62344325, 63498401, 66345221, 66571141, 67194401, 67421761, 67763521, 68449633, 68908961, 69024033, 70180033, 71170181, 72049601, 73289861, 74182241, 74540705, 74720261, 75500833, 75681541, 75802133, 75983201, 78172865, 79094405, 79156033, 79341061, 80766785, 81390625, 81515681, 82079621, 84482133, 84800833, 84928481, 85504085, 88476421, 89587745, 92629633, 93163841, 94236865, 95790101, 96809921, 97903681.