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

%I A057821 #44 Jan 26 2023 20:01:32
%S A057821 1,5,9,5,21,29,9,5,9,17,45,161,165,269,285,17,45,233,9,17,321,317,633,
%T A057821 677,405,437,189,1385,69,209,9,641,849,137,45,401,381,437,1965,2201,
%U A057821 741,1493,573,857,1485,5297,2709,161,465,473,1269,4805,789
%N A057821 a(n) is the least nonnegative integer k such that 2^n - k is a safe prime.
%C A057821 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
%H A057821 Mark Andreas, <a href="/A057821/b057821.txt">Table of n, a(n) for n = 3..5120</a> (first 3070 terms from Artsiom Palkounikau)
%o A057821 (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
%o A057821 (Python)
%o A057821 from sympy import isprime
%o A057821 def a(n):
%o A057821     k=0
%o A057821     while True:
%o A057821         k+=1
%o A057821         if isprime(2**n - k) and isprime((2**n - k - 1)//2): return k
%o A057821 print([a(i) for i in range(3, 21)]) # _Indranil Ghosh_, Jun 12 2017, after PARI code by _Michel Marcus_
%Y A057821 Cf. A005385, A013603, A243916.
%K A057821 nonn
%O A057821 3,2
%A A057821 _Warren D. Smith_, Nov 23 2000