A359640 -id:A359640 - cp's OEIS frontend

A359639 a(n) is the least odd prime not in A001359 such that all subsequent composites in the gap up to the next prime have at least n odd prime factors, counted with multiplicity.

97, 1999, 101527, 6666547, 272572999, 3819770107, 410274361249

Offset: 2

Hugo Pfoertner, Jan 16 2023

			a(2) = 97: 98 = 2*7^2, 99 = 3^2*11, 100 = 2^2*5^2 have 2 or 3 odd prime factors, so the minimum 2 is achieved.
a(3) = 1999: 2000 has the 3 odd prime factors 5^3, 2001 = 3*23*29, 2002 = 2*7*11*13.

Cf. A001222, A001359, A087436, A359637, A359640.

a087436(n) = bigomega (n >> valuation (n, 2));
a359639(maxp) = {my(k=2,pp=5); forprime (p=7, maxp, my(mi=oo); if (p-pp>2, for (j=pp+1, p-1, my(mo=a087436(j)); if (mo=k, print1(pp,", "); k++)); pp=p)};
a359639(3*10^8)

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.

Original entry on oeis.org

307, 8929, 992263, 229658167, 28674536239

Offset: 2

Hugo Pfoertner, Jan 17 2023

			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.

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

obi(x,m=0) = {my (x2=x>>valuation(x,2), o=omega(x2)); if (o2, for (j=pp+1, p-1, my (mo=obi(j)); if (mo

cp's OEIS Frontend

A359639 a(n) is the least odd prime not in A001359 such that all subsequent composites in the gap up to the next prime have at least n odd prime factors, counted with multiplicity.

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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.

Views

Author

Keywords

Examples

Crossrefs

Programs

PARI