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Least b such that b^(2^n) + 1 is an odd Pierpont prime (A005109).
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%I #7 Dec 18 2020 13:50:26

%S 2,2,2,2,2,54,162,8310407949893763072,46438023168,65229815808,

%T 396718580736,629856,152461794335880672662217818112

%N Least b such that b^(2^n) + 1 is an odd Pierpont prime (A005109).

%C Every term is even (A005843) and 3-smooth (A003586).

%C For n = 0, 1, 2, 3, 4, 7, 8, 9, 12, ..., the corresponding number b^(2^n) + 1 is also a Proth prime (A080076), while for n = 5, 6, 10, 11, ..., it is a non-Proth.

%C The form b^(2^n) + 1 is called a generalized Fermat number.

%e a(7) corresponds to prime 8310407949893763072^128 + 1 = (2^47*3^10)^128 + 1.

%Y Cf. A005109, A056993, A334053.

%K nonn,hard,more

%O 0,1

%A _Jeppe Stig Nielsen_, Nov 16 2020