

A057673


Smallest prime p such that 2^n  p is a prime.


1



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
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OFFSET

0,1


COMMENTS

The absolute value is relevant only for first two terms, 2^0a(0) = 13 = 2, 2^1a(1) = 25 = 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


LINKS

Table of n, a(n) for n=0..72.


EXAMPLE

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=12819, so q(n)=19.


MATHEMATICA

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


PROG

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


CROSSREFS

Analog of A056206. Cf. A056208, A057662.
Sequence in context: A059246 A091276 A076562 * A200109 A156060 A205701
Adjacent sequences: A057670 A057671 A057672 * A057674 A057675 A057676


KEYWORD

nonn


AUTHOR

Labos Elemer, Oct 19 2000


EXTENSIONS

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


STATUS

approved



