A359641 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, all with exponent 1.

307, 8929, 992263, 229658167, 28674536239

Offset

2,1

Links

Table of n, a(n) for n=2..6.

Example

a(3) = 8929: 8930 = 2*5*19*47, 8931 = 3*13*229, 8932 = 2^2*7*11*29;
a(6) = 28674536239: a(6)+1 = 2^4*5*7*31*43*107*359, a(6)+2 = 3*13*23*151*269*787, a(6)+3 = 2*11*17*19*37*191*571.

Prog

(PARI) obi(x, m=0) = {my (x2=x>>valuation(x, 2), o=omega(x2)); if (o<m, return(0), if (bigomega(x2)-o, 0, o))};
a359641(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=obi(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)};
a359641(3*10^8)

Crossrefs

Cf. A001222, A001359, A087436, A285800, A359640.

Sequence in context: A359640 A118284 A234030 * A309566 A118843 A224675

Adjacent sequences: A359638 A359639 A359640 * A359642 A359643 A359644

Keyword

nonn,hard,more

Author

Hugo Pfoertner, Jan 17 2023

Status

approved