A051887 - OEIS

A051887

Minimal and special 2k-Germain primes, where 2k is in A002110 (primorial numbers).

2, 2, 2, 2, 2, 5, 17, 11, 11, 11, 2, 23, 7, 43, 19, 3, 5, 2, 7, 3, 61, 53, 2, 41, 47, 2, 5, 7, 31, 2, 47, 13, 113, 7, 137, 103, 43, 41, 97, 3, 173, 97, 41, 13, 97, 59, 29, 53, 3, 107, 127, 197, 3, 487, 433, 31, 281, 587, 7, 89, 41, 47, 193, 239, 41, 7, 31, 67

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

a(n) is the minimal prime p such that primorial(n)*p + 1 is also prime.

While p is in A005384, the primorial(n)*p + 1 primes are in A051902 (primorial-safe primes).

Analogous to or subset of A051686, where the even numbers are 2, 6, ..., A002110(n), ...

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = (A051902(n)-1)/A002110(n). - Amiram Eldar, Feb 25 2025

EXAMPLE

a(25) = 47 because primorial(25)*47 + 1 is also prime and minimal with this property: primorial(25)*47 + 1 = 47*2305567963945518424753102147331756070 + 1 = 108361694305439365963395800924592535291 is a minimal prime. The first 6 terms (2,2,2,2,2,5) correspond to first entries in A005384, A007693, A051645, A051647, A051653, A051654, respectively.

MATHEMATICA

Table[p = 2; While[! PrimeQ[Product[Prime@ i, {i, n}] p + 1], p = NextPrime@ p]; p, {n, 68}] (* Michael De Vlieger, Jun 29 2017 *)

PROG

(PARI) a(n) = {my(p = 2, r = vecprod(primes(n))); while(!isprime(p * r + 1), p = nextprime(p+1)); p; } \\ Amiram Eldar, Feb 25 2025

CROSSREFS

Cf. A002110, A005384, A005385, A051686, A007693, A051886, A051888, A051902.

Sequence in context: A241148 A172414 A266995 * A139516 A225953 A278247

Adjacent sequences: A051884 A051885 A051886 * A051888 A051889 A051890

KEYWORD

nonn,changed

AUTHOR

Labos Elemer, Dec 15 1999

EXTENSIONS

More terms from Michael De Vlieger, Jun 29 2017

STATUS

approved