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A345014
a(n) is the least nonnegative integer k such that 2^n - k is a Sophie Germain prime.
1
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
1,3
LINKS
FORMULA
a(n) = (A057821(n+1) + 1)/2.
MATHEMATICA
Table[k=0; While[!(PrimeQ[p=2^n-k]&&PrimeQ[2p+1]), k++]; k, {n, 58}] (* Giorgos Kalogeropoulos, Sep 15 2021 *)
PROG
(Python)
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)])
(PARI) a(n) = my(k=0, p); while (!(isprime(p=2^n-k) && isprime(2*p+1)), k++); k; \\ Michel Marcus, Sep 15 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Artsiom Palkounikau, Sep 15 2021
STATUS
approved