A381725 Numbers k such that 5^k - 4^k is a semiprime.

2, 5, 7, 11, 13, 19, 31, 41, 79, 83, 113, 157, 173, 233, 281, 317, 359, 373

Offset: 1

Author

Zak Seidov and Robert Israel, Mar 05 2025

Keywords

• nonn
• hard
• more

Comments

Are all terms prime? Any term that is not a prime must be the square of a member of A059802.

Examples

			a(3) = 7 is a term because 5^7 - 4^7 = 61741 = 29 * 2129 with 29 and 2129 prime.
		

Links

• Status of 5^449-4^449 in factordb.com.

Crossrefs

Cf. A001222, A001358, A005060, A059802, A082869.

Programs

Maple

filter:= n -> numtheory:-bigomega(5^n - 4^n):
select(filter, [2,seq(i,i=3..120,2]);

Formula

A001222(A005060(a(n))) = 2.

Extensions

a(14)-a(18) from Jinyuan Wang, Mar 05 2025