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%I #20 Nov 29 2021 01:39:29
%S 3,5,2,3,3,3,3,19,5,3,3,19,3,13,3,19,17,13,5,19,3,19,3,37,3,61,5,79,
%T 89,3,41,19,5,79,41,31,5,31,107,7,167,31,11,67,17,139,167,127,59,139,
%U 71,139,47,379,53,67,5,13,137,607,107,31,167,409,59,79,5,19,23,19,71,577,107
%N Smallest prime p such that |2^n - p| is a prime.
%C The absolute value is relevant only for first two terms, 2^0-a(0) = 1-3 = -2, 2^1-a(1) = 2-5 = -3. According to Goldbach's conjecture, every even number > 2 is the sum of two primes, which implies that for all further terms, a(n) < 2^n. - _M. F. Hasler_, Jan 13 2011
%H Hugo Pfoertner, <a href="/A057673/b057673.txt">Table of n, a(n) for n = 0..5000</a>
%e n=7, 2^n=128. The smallest terms subtracted from 128 resulting in a prime are 1,15,19,... Neither 1 nor 15 are primes but 19 is a prime. It gives 109=128-19, so a(n)=19.
%t f[n_] := Block[{p = 2}, While[! PrimeQ[2^n - p], p = NextPrime@ p]; p]; Array[f, 60, 0]
%o (PARI) A057673(n)=forprime( p=1,default(primelimit), ispseudoprime(abs(2^n-p))& return(p))
%Y Analog of A056206. Cf. A056208, A057662.
%K nonn
%O 0,1
%A _Labos Elemer_, Oct 19 2000
%E Offset corrected and initial term added by _M. F. Hasler_, Jan 13 2011
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