A057673 Smallest prime p such that |2^n - p| is a prime.

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, 89, 3, 41, 19, 5, 79, 41, 31, 5, 31, 107, 7, 167, 31, 11, 67, 17, 139, 167, 127, 59, 139, 71, 139, 47, 379, 53, 67, 5, 13, 137, 607, 107, 31, 167, 409, 59, 79, 5, 19, 23, 19, 71, 577, 107

Offset: 0

Author

Labos Elemer, Oct 19 2000

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

• Hugo Pfoertner, Table of n, a(n) for n = 0..5000

Crossrefs

Analog of A056206. Cf. A056208, A057662.

Programs

Mathematica

f[n_] := Block[{p = 2}, While[! PrimeQ[2^n - p], p = NextPrime@ p]; p]; Array[f, 60, 0]

PARI

A057673(n)=forprime( p=1,default(primelimit), ispseudoprime(abs(2^n-p))& return(p))

Extensions

Offset corrected and initial term added by M. F. Hasler, Jan 13 2011