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