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a-pointer prime  and  Proth n.

First numbers that belong to both sets:

13, 1153, 1409, 36353, 102913, 115201, 301057, 329729, 384001, 520193, 959489, 3604481, 4452353, 4632577, 6234113, 7057409, 11456513, 13037569, 22069249, 26337281, 34988033, 35045377, 52314113, 58163201, 61317121, 61431809, 62423041, 64208897, 69304321, 85426177, 90439681, 93831169, 100335617, 104759297, 121946113, 152371201, 162168833, 170311681, 180535297, 215482369, 217612289, 228212737, 260571137, 298221569, 391708673, 403603457, 411107329, 568000513, 657063937, 658145281, 678297601, 710934529, 715128833, 817070081, 820150273, 820346881, 846790657, 879001601, 893059073, 1021444097, 1040842753, 1136263169, 1193803777, 1248133121, 1341063169, 1374289921, 1541079041, 1580531713, 1616314369, 1693843457, 1762787329, 1830092801, 1905131521, 1974403073, 2040856577, 2055733249, 2200240129, 2214002689, 2247032833, 2255945729, 2282618881, 2316828673, 2370306049, 2440560641, 2641428481, 2730295297, 2743468033, 2792292353, 2900033537, 2928345089, 3052339201, 3090087937, 3120955393, 3131441153, 3193700353, 3281846273, 3313041409, 3348889601, 3361865729, 3385262081, 3406102529, 3434151937, 3444244481, 3456040961, 3506307073, 3680370689, 3733258241, 4000382977, 4021485569, 4027187201, 4031840257, 4043243521, 4075159553, 4105961473, 4187619329, 4240310273, 4646502401, 4847173633, 5016518657, 5053218817, 5063704577, 5364514817, 5413273601, 5414060033, 5492310017, 5753929729, 5780668417, 6476660737, 6493175809, 6731333633, 6923747329, 7056654337, 7267418113, 7311065089, 7614627841, 7664173057, 7802847233, 8212185089, 8242462721, 8297512961, 8323072001, 8362524673, 8392409089, 8511160321, 9144631297, 9177137153, 9241231361, 9339273217, 9666035713, 9767878657.