Artsiom Palkounikau - cp's OEIS frontend

User: Artsiom Palkounikau

Artsiom Palkounikau has authored 2 sequences.

A345014 a(n) is the least nonnegative integer k such that 2^n - k is a Sophie Germain prime.

0, 1, 3, 5, 3, 11, 15, 5, 3, 5, 9, 23, 81, 83, 135, 143, 9, 23, 117, 5, 9, 161, 159, 317, 339, 203, 219, 95, 693, 35, 105, 5, 321, 425, 69, 23, 201, 191, 219, 983, 1101, 371, 747, 287, 429, 743, 2649, 1355, 81, 233, 237, 635, 2403, 395, 1125, 1997, 69, 9005

Offset: 1

Artsiom Palkounikau, Sep 15 2021

nonn

Artsiom Palkounikau, Table of n, a(n) for n = 1..3072

Cf. A005384, A057821, A013603, A243916.

Table[k=0;While[!(PrimeQ[p=2^n-k]&&PrimeQ[2p+1]),k++];k,{n,58}] (* Giorgos Kalogeropoulos, Sep 15 2021 *)

a(n) = my(k=0,p); while (!(isprime(p=2^n-k) && isprime(2*p+1)), k++); k; \\ Michel Marcus, Sep 15 2021

from sympy import isprime
def a(n):
    k = 0
    while True:
        if isprime(2 ** n - k) and isprime(2 * (2 ** n - k) + 1):
            return k
        k += 1
print([a(i) for i in range(1, 21)])

a(n) = (A057821(n+1) + 1)/2.

A335313 Smallest k such that 2^(3*2^n) - k is a safe prime.

Original entry on oeis.org

1, 5, 17, 317, 5297, 3449, 41213, 59057, 468857, 1503317, 1103717, 40207829, 154474973, 1162354373, 18153497

Offset: 0

Artsiom Palkounikau, Jun 01 2020

			a(1) = 5 because 2^(3*2^1)-5 = 2^6-5 = 59 is the largest safe prime less than 64.

Cf. A005385 (safe primes), A057821, A181356.

a(n) = {my(k=0); while (!(isprime(p=2^(3*2^n) - k) && isprime((p-1)/2)), k++); k;} \\ Michel Marcus, Jun 01 2020

from sympy import isprime, prevprime
def A335313(n):
    m = 2**(3*2**n)
    p = prevprime(m)
    while not isprime((p-1)//2):
        p = prevprime(p)
    return m-p # Chai Wah Wu, Jul 09 2020

a(13) from Artsiom Palkounikau, Oct 13 2021

a(14) from Mark Andreas, Jun 06 2022

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User: Artsiom Palkounikau

A345014 a(n) is the least nonnegative integer k such that 2^n - k is a Sophie Germain prime.

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