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%I #4 Jan 30 2023 12:29:56
%S 307,1999,101527,7146697,272572999,4809363523
%N 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.
%e a(2) = 307: 308 = 2^2*7*11, 309 = 3*103, 310 = 2*5*31, all have exactly 2 odd prime factors.
%o (PARI) a087436(n) = bigomega (n >> valuation (n, 2));
%o 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)};
%o a359640(3*10^8)
%Y Cf. A001222, A001359, A087436, A359637, A359639.
%K nonn,hard,more
%O 2,1
%A _Hugo Pfoertner_, Jan 16 2023
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