A374006 Product of the first n primes greater than or equal to n.

1, 2, 6, 105, 5005, 85085, 7436429, 215656441, 35336848261, 1448810778701, 62298863484143, 2928046583754721, 832363787945546597, 50774191064678342417, 18579448222667298067513, 1356299720254712758928449, 107147677900122307955347471, 8893257265710151560293840093

Offset

0,2

Comments

This sequence came up in the course of a currently ongoing investigation into Singmaster's conjecture by a group including the author of this sequence.

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = Product_{i=1+pi(n-1)..n+pi(n-1)} prime(i).

a(n) = A272899(n) <=> n in A141468.

Example

a(4) is the product of the first four primes greater than or equal to 4: 5*7*11*13 = 5005.

Maple

a:= n-> mul((nextprime@@i)(n-1), i=1..n):
seq(a(n), n=0..17);  # Alois P. Heinz, Jun 24 2024

Mathematica

a[n_]:=Product[Prime[i], {i, 1+PrimePi[n-1], n+PrimePi[n-1]}]; Array[a, 18, 0] (* Stefano Spezia, Jun 25 2024 *)

Prog

(PARI) a(n) = if (n==0, 1, my(p=nextprime(n)); vecprod(primes([p, prime(primepi(p)+n-1)]))); \\ Michel Marcus, Jun 25 2024

Crossrefs

Cf. A000040, A000720, A141468, A272899.

Sequence in context: A099790 A294906 A284262 * A287935 A357090 A181036

Adjacent sequences: A374003 A374004 A374005 * A374007 A374008 A374009

Keyword

nonn,easy

Author

Jesse Hammer, Jun 24 2024

Status

approved