A357253 a(n) is the largest prime < 6*n.

5, 11, 17, 23, 29, 31, 41, 47, 53, 59, 61, 71, 73, 83, 89, 89, 101, 107, 113, 113, 113, 131, 137, 139, 149, 151, 157, 167, 173, 179, 181, 191, 197, 199, 199, 211, 211, 227, 233, 239, 241, 251, 257, 263, 269, 271, 281, 283, 293, 293, 293, 311, 317, 317, 317, 331, 337, 347, 353

Offset: 1

Author

Michel Marcus, Sep 20 2022

Keywords

• nonn
• easy

Comments

Largest prime that can be obtained after n rolls of a fair 6-sided die.

Examples

			a(11) = 61 as the largest prime <= 6*11 = 66 is 61; each of 62, 63, 64, 65 and 66 are not prime. - _David A. Corneth_, Sep 20 2022
		

Links

• Noga Alon and Yaakov Malinovsky, Hitting a prime in 2.43 dice rolls (on average), arXiv:2209.07698 [math.PR], 2022.

Crossrefs

Cf. A002476, A007528, A007917, A008588, A060308, A118749, A151799.

Programs

Maple

a:= n-> prevprime(6*n):
seq(a(n), n=1..60);  # Alois P. Heinz, Sep 20 2022

Mathematica

a[n_] := NextPrime[6*n, -1]; Array[a, 60] (* Amiram Eldar, Sep 20 2022 *)

PARI

a(n) = precprime(6*n);

Python

from sympy import prevprime
def A357253(n): return prevprime(6*n) # Chai Wah Wu, Sep 20 2022

Formula

a(n) = A007917(A008588(n)).

a(n) = A151799(A008588(n)), since 6*n is never prime.