A338931 Least b such that b^(2^n) + 1 is an odd Pierpont prime (A005109).

2, 2, 2, 2, 2, 54, 162, 8310407949893763072, 46438023168, 65229815808, 396718580736, 629856, 152461794335880672662217818112

Offset

0,1

Comments

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

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.

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

Links

Table of n, a(n) for n=0..12.

Example

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

Crossrefs

Cf. A005109, A056993, A334053.

Sequence in context: A029665 A256223 A056993 * A057331 A334053 A270374

Adjacent sequences: A338928 A338929 A338930 * A338932 A338933 A338934

Keyword

nonn,hard,more

Author

Jeppe Stig Nielsen, Nov 16 2020

Status

approved