A052299 - OEIS

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

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OFFSET

2,2

LINKS

Amiram Eldar, Table of n, a(n) for n = 2..10000

EXAMPLE

For n = 81: prime(81) = 419, prime(82) = 421. The intermediate range of composites includes only 420 = 4*3*5*7 having 4 distinct 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, A052298.

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