A359638 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 prime factors, counted with multiplicity.
601, 1429, 81547, 248749, 27140749, 310314157, 3566181247
Offset: 3
Programs
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PARI
a359638(maxp) = {my (k=3, pp=3); forprime (p=5, maxp, my (mi=oo, ma=0); if (p-pp>2, for (j=pp+1, p-1, my(mo=bigomega(j)); if(mo