A052299 Minimal number of distinct prime factors of any composite number between n-th and (n+1)-st primes.

1, 2, 1, 2, 1, 2, 2, 1, 3, 1, 2, 3, 2, 1, 2, 3, 1, 2, 2, 2, 1, 2, 2, 2, 3, 2, 2, 2, 1, 1, 2, 3, 2, 3, 2, 2, 2, 1, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 3, 1, 1, 2, 2, 3, 2, 2, 3, 1, 2, 2, 3, 2, 2, 2, 1, 3, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 1, 3, 1, 2, 2, 2, 2, 4, 2, 2

Offset

2,2

Links

Table of n, a(n) for n=2..106.

Example

n=81: p(81)=419, p(82)=421. The intermediate range of composites includes only 420=4*3*5*7 having 4 prime-factors, so a(81)=4;

Mathematica

Min[PrimeNu[Range[#[[1]]+1, #[[2]]-1]]]&/@Partition[Prime[ Range[ 2, 110]], 2, 1] (* Harvey P. Dale, Mar 31 2012 *)

Crossrefs

Cf. A052180, A052248.

Sequence in context: A274354 A083870 A368779 * A071854 A183025 A072410

Adjacent sequences: A052296 A052297 A052298 * A052300 A052301 A052302

Keyword

nonn

Author

Labos Elemer, Feb 09 2000

Extensions

Offset corrected by Sean A. Irvine, Nov 04 2021

Status

approved