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

Author

Warren D. Smith, Nov 23 2000

Keywords

• nonn

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)

Crossrefs

Cf. A005385, A013603, A243916.

Programs

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