A101047 a(n) is the least k such that k*(prime(n)#)^prime(n)-1 is prime, where prime(n)# is the n-th primorial.

1, 2, 3, 15, 13, 6, 12, 23, 44, 5, 33, 153, 82, 63, 133, 376, 162, 340, 1009, 30, 9, 12, 2818, 843, 1343, 1348, 42, 125, 1260, 2135, 1856, 2049, 2664, 4585, 2253, 1664, 5397, 2859, 4382, 620, 599, 1072

Offset

1,2

Links

Table of n, a(n) for n=1..42.

Example

a(1) = 1 since 1*2^2 - 1 = 3 is prime.
a(2) = 2 since 2*(2*3)^3 - 1 = 431 is prime.

Mathematica

a[n_] := Module[{k = 1, p = Product[Prime[i], {i, 1, n}]^Prime[n]}, While[!PrimeQ[k*p-1], k++]; k]; Array[a, 50] (* Amiram Eldar, Jul 17 2021 *)

Prog

(Python)
from sympy import isprime, prime, primorial
def a(n):
    k, t = 1, primorial(n)**prime(n)
    while True:
        if isprime(k*t - 1): return k
        k += 1
print([a(n) for n in range(1, 15)]) # Michael S. Branicky, Jan 29 2022

Crossrefs

Cf. A002110.

Sequence in context: A075244 A342567 A088030 * A251618 A309765 A238691

Adjacent sequences: A101044 A101045 A101046 * A101048 A101049 A101050

Keyword

nonn,more

Author

Pierre CAMI, Jan 21 2005

Extensions

a(27)-a(32) from Amiram Eldar, Jul 17 2021

a(33)-a(34) from Michael S. Branicky, Jan 29 2022

a(35)-a(36) from Michael S. Branicky, Feb 03 2022

a(37)-a(42) from Michael S. Branicky, May 14 2023

Status

approved