cp's OEIS Frontend

For n > 0, every n-fold repetition of a(n) is a "powerful" arithmetic progression with difference 0; e.g., for n = 4 we get a(4) = 16777216 and in the generated repeating sequence of length 4 the k-th term is a k-th power (1 <= k <= n): 16777216 = 16777216^1, 16777216 = 4096^2, 16777216 = 256^3, 16777216 = 64^4. - Martin Renner, Aug 16 2017

From Jianing Song, Jul 20 2021: (Start)

Let F_q be the finite field with q elements, then in F_a(n), every polynomial of degree at most n splits into linear factors.

Union_{n>=0} F_a(n) is the algebraic clousre of F_2, which is the unique algebraically closed field with characteristic 2 and transcendence degree 0 (note that an algebraically closed field is uniquely determined by its characteristic and transcendence degree). Union_{n>=0} F_(2^lcm(1,2,...,n)) = Union_{n>=0} F_A178981(n) gives the same field.

Obviously, here 2 can be replaced by any prime p provided that {a(n)} is defined as a(n) = p^(n!). (End)

For n >= 1, the number of digits of a(n) is A317873(n). - Martin Renner, Mar 24 2024

The next term (a(6)) has 504 digits. - Harvey P. Dale, Apr 01 2013

a(6) has 434 digits.

The exponential growth in the number of permutations of n elements.

Next term is too big to be included.