A051453 Prime powers such that 1 + lcm(1,2,...,p^w) is prime.

1, 2, 3, 4, 5, 7, 9, 19, 25, 31, 47, 89, 127, 139, 1369, 2251, 3271, 4253, 4373, 4549, 5449, 13331, 37123, 55291, 79633, 105653, 211151, 227993

Offset

1,2

Links

Table of n, a(n) for n=1..28.

Example

1 + lcm(1,2,..,89) = 718766754945489455304472257065075294401 is prime.

Prog

(PARI) ispp(n) = isprimepower(n) || n==1;
isok(n) = ispp(n) && ispseudoprime(1+lcm([1..n])); \\ Michel Marcus, Aug 26 2019

Crossrefs

Cf. A000961, A003418, A049536, A049537, A075059.

Sequence in context: A282895 A293535 A261170 * A357166 A302940 A272072

Adjacent sequences: A051450 A051451 A051452 * A051454 A051455 A051456

Keyword

nonn,more

Author

Labos Elemer

Extensions

Corrected and extended by Wouter Meeussen, Apr 18 2003

a(18)-a(22) from Jinyuan Wang, May 02 2020

a(23)-a(24) from Michael S. Branicky, Apr 22 2023

a(25)-a(26) from Michael S. Branicky, Jul 04 2025

a(27)-a(28) from Jan Popelka, Apr 21 2026

Status

approved