A385315 Smallest number k such that both k^n - 1 and k^n + 1 have n prime factors, counted with repetitions.

4, 12, 66, 920, 26, 132, 79, 17958, 53, 693, 4181, 122160, 29791, 32318, 971

Offset: 1

Author

Jean-Marc Rebert, Aug 12 2025

Keywords

• nonn
• more
• changed

Examples

			a(1) = 4, because 4^1 - 1 = 3  and 4^1 + 1 = 5, and no lesser number has this property.
See the Links section for more examples.
		

Links

• Jean-Marc Rebert, Factorizations of k^n-1 and k^n+1

Crossrefs

Cf. A001222, A001358, A014612, A078840, A385591.

Programs

PARI

a(n) = my(k=2, kn=k^n); while ((bigomega(kn-1)!=n) || (bigomega(kn+1)!=n), k++;kn=k^n); k; \\ Michel Marcus, Aug 18 2025