A118749 -id:A118749 - cp's OEIS frontend

A118750 a(n) = product[k=1..n] P(k), where P(k) is the largest prime <= 3*k. a(n) = product[k=1..n] A118749(k).

3, 15, 105, 1155, 15015, 255255, 4849845, 111546435, 2565568005, 74401472145, 2306445636495, 71499814731345, 2645493145059765, 108465218947450365, 4664004414740365695, 219208207492797187665, 10302785752161467820255

Offset: 1

Jonathan Vos Post, Apr 29 2006

Differs from (after first term) A048599 "Partial products of the sequence (A001097) of twin primes" after 8th term. Differs from (after first term) A070826 "One half of product of first n primes A000040" after 9th term. Analogous to A118455 a(1)=1. a(n) = product{k=1..n} P(k), where P(k) is the largest prime <= k.

Cf. A020482, A049653, A060266-A060268, A060264, A060265, A060308, A118455, A118456, A118748.

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

Original entry on oeis.org

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

Michel Marcus, Sep 20 2022

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

			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

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

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

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

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

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

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

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

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

cp's OEIS Frontend

A118750 a(n) = product[k=1..n] P(k), where P(k) is the largest prime <= 3*k. a(n) = product[k=1..n] A118749(k).

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

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