A359639 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 odd prime factors, counted with multiplicity.

97, 1999, 101527, 6666547, 272572999, 3819770107, 410274361249

Offset

2,1

Links

Table of n, a(n) for n=2..8.

Example

a(2) = 97: 98 = 2*7^2, 99 = 3^2*11, 100 = 2^2*5^2 have 2 or 3 odd prime factors, so the minimum 2 is achieved.
a(3) = 1999: 2000 has the 3 odd prime factors 5^3, 2001 = 3*23*29, 2002 = 2*7*11*13.

Prog

(PARI) a087436(n) = bigomega (n >> valuation (n, 2));
a359639(maxp) = {my(k=2, pp=5); forprime (p=7, maxp, my(mi=oo); if (p-pp>2, for (j=pp+1, p-1, my(mo=a087436(j)); if (mo<k, mi=0; break); mi=min(mo, mi)); if (mi>=k, print1(pp, ", "); k++)); pp=p)};
a359639(3*10^8)

Crossrefs

Cf. A001222, A001359, A087436, A359637, A359640.

Sequence in context: A162542 A241968 A020538 * A075665 A012839 A379508

Adjacent sequences: A359636 A359637 A359638 * A359640 A359641 A359642

Keyword

nonn,hard,more

Author

Hugo Pfoertner, Jan 16 2023

Status

approved