A057821 a(n) is the least nonnegative integer k such that 2^n - k is a safe prime.

1, 5, 9, 5, 21, 29, 9, 5, 9, 17, 45, 161, 165, 269, 285, 17, 45, 233, 9, 17, 321, 317, 633, 677, 405, 437, 189, 1385, 69, 209, 9, 641, 849, 137, 45, 401, 381, 437, 1965, 2201, 741, 1493, 573, 857, 1485, 5297, 2709, 161, 465, 473, 1269, 4805, 789

Offset

3,2

Comments

Previous name was: "Useful safe primes: a(n) = least nonnegative integer k such that 2^n - k is prime and (2^n-k-1)/2 is also prime". The resulting sequence of 2^n-k terms: 7, 11, 23, 59, 107, ..., are thus the largest safe primes smaller than 2^n (A243916), a subsequence of A005385. - Michel Marcus, Jan 08 2014

Links

Mark Andreas, Table of n, a(n) for n = 3..5120 (first 3070 terms from Artsiom Palkounikau)

Prog

(PARI) a(n) = {my(k=0); until (isprime(2^n-k) && isprime((2^n-k-1)/2), k++); return (k); } \\ Michel Marcus, Jun 29 2013
(Python)
from sympy import isprime
def a(n):
    k=0
    while True:
        k+=1
        if isprime(2**n - k) and isprime((2**n - k - 1)//2): return k
print([a(i) for i in range(3, 21)]) # Indranil Ghosh, Jun 12 2017, after PARI code by Michel Marcus

Crossrefs

Cf. A005385, A013603, A243916.

Sequence in context: A355178 A010720 A094389 * A133742 A134879 A051158

Adjacent sequences: A057818 A057819 A057820 * A057822 A057823 A057824

Keyword

nonn

Author

Warren D. Smith, Nov 23 2000

Status

approved