A051833 Primes of form (2*10^(5n) - 10^(4n) + 2*10^(3n) + 10^(2n) + 10^n + 1)/3.

2, 64037, 66666663333334000000033333336666667

Offset: 1

Author

G. L. Honaker, Jr., Dec 11 1999

Keywords

• hard
• nonn

Comments

The Baxter-Hickerson function provides a number whose cube lacks zeros.

Next term has 665 digits and is in b-file.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..4
• Ed Pegg, Jr., Fun with numbers.
• Eric Weisstein's World of Mathematics, Baxter-Hickerson Function.

Crossrefs

Cubes: A051750, A051751, A051832, A052044, A052045, A052427.

Squares: A052040, A052041, A052042, A052043.

Programs

Mathematica

Select[Table[(2*10^(5*n) - 10^(4*n) + 2*10^(3*n) + 10^(2*n) + 10^n + 1)/3, {n, 0, 150}], PrimeQ] (* Amiram Eldar, Jul 18 2025 *)

Formula

a(n) = A052427(A051832(n)). - Amiram Eldar, Jul 18 2025