A359637 a(n) is the least odd prime not in A001359 such that all subsequent composites in the gap up to the next prime have at least n prime factors, counted with multiplicity.

7, 97, 349, 13309, 33613, 5594749, 84477247, 1524981247, 60924074749

Offset: 2

Author

Hugo Pfoertner, Jan 16 2023

Keywords

• nonn
• hard
• more

Examples

			a(2) = 7: 8 = 2^3, 9 = 3^2, 10 = 2*5 all have at least the minimum number of 2 prime factors;
a(3) = 97: 98 = 2*7^2, 99 = 3^2*11, 100 = 2^2*5^2 have a minimum of 3 prime factors;
a(4) = 349: 350 = 2*5^2*7, 351 = 3^3*13, 352 = 2^5*11 have a minimum of 4 prime factors.
		

Crossrefs

Cf. A001222, A001359, A062502, A359636.

Programs

PARI

a359637(maxp) = {my (k=2, pp=3); forprime (p=5, maxp, my(mi=oo); if (p-pp>2, for (j=pp+1, p-1, my(mo=bigomega(j)); if (mo=k, print1(pp,", "); k++)); pp=p)};
a359637(10^8)