A359640 a(n) is the least odd prime not in A001359 such that all subsequent composites in the gap up to the next prime have exactly n odd prime factors, counted with multiplicity.

307, 1999, 101527, 7146697, 272572999, 4809363523

Offset

2,1

Links

Table of n, a(n) for n=2..7.

Example

a(2) = 307: 308 = 2^2*7*11, 309 = 3*103, 310 = 2*5*31, all have exactly 2 odd prime factors.

Prog

(PARI) a087436(n) = bigomega (n >> valuation (n, 2));
a359640(maxp) = {my(k=2, pp=5); forprime (p=7, maxp, my(mi=oo, ma=0); if (p-pp>2, for (j=pp+1, p-1, my(mo=a087436(j)); if (mo<k, mi=ma=0; break); mi=min(mo, mi); ma=max(mo, ma)); if (mi==k && ma==k, print1(pp, ", "); k++)); pp=p)};
a359640(3*10^8)

Crossrefs

Cf. A001222, A001359, A087436, A359637, A359639.

Sequence in context: A142572 A204477 A176091 * A118284 A234030 A359641

Adjacent sequences: A359637 A359638 A359639 * A359641 A359642 A359643

Keyword

nonn,hard,more

Author

Hugo Pfoertner, Jan 16 2023

Status

approved