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

a(n) is A145571(n) (a decimal number with digits only from {0,1}) read as base 2 number converted back into decimal notation.

The sequence of digit lengths is 1,1,2,8,37,217,1518,... (see A317873).

This sequence gives the numerators of the partial sums for the constant A092874 (called there "binary" Liouville number). See the B(n) formula below. - Wolfdieter Lang, Apr 10 2024