A057821 - OEIS

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

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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