A067024 Smallest prime p such that p+2 has exactly n distinct prime factors.

2, 13, 103, 1153, 15013, 255253, 4849843, 111546433, 4360010653, 100280245063, 5245694198743, 152125131763603, 7149881192889433, 421842990380476663, 16294579238595022363, 1106494163767990292293, 74135108972455349583763, 4632891063696575353839163, 278970415063349480483707693, 24012274383139350058948392193

Offset

1,1

Links

Sean A. Irvine, Table of n, a(n) for n = 1..58 (terms 1..38 from Michael S. Branicky)

Michael S. Branicky, Python program

Sean A. Irvine, Java program (github)

Formula

a(n) = Min_{p in A000040 ; A001221(p+2) = n}.

Example

For n = 1,...,7 the factors of 2+a(n) are as follows: 2*2, 3*5, 3*5*7, 3*5*7*11, 3*5*7*11*13, 3*5*7*11*13*17, 3*5*7*11*13*17*19; i.e., a(n) = A002110(n+1)/2 which is prime for n = 2,...,7.

Prog

(Python) # see linked program

Crossrefs

Cf. A000040, A001221, A002110, A053705, A067023.

Sequence in context: A007809 A259146 A103513 * A371583 A083062 A204261

Adjacent sequences: A067021 A067022 A067023 * A067025 A067026 A067027

Keyword

nonn

Author

Labos Elemer, Dec 29 2001

Extensions

a(8)-a(15) from Donovan Johnson, Jan 21 2009

a(16) and beyond from Michael S. Branicky, Feb 07 2023

Status

approved