

A174269


Numbers n such that exactly one of 2^n  1 and 2^n + 1 is a prime.


3



0, 1, 3, 4, 5, 7, 8, 13, 16, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917
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OFFSET

1,3


COMMENTS

Apart from the first term, all terms are primes (Mersenne exponents) or powers of two (Fermat exponents). The sequence consists of all members of A000043 and A092506, apart from 2.  Charles R Greathouse IV, Mar 20 2010
Numbers n such that one of 2^n+1 or 2^n1 is prime, but not both.  R. J. Mathar, Mar 29 2010
The sequence "Numbers n such that 2^n + (1)^n is a prime" gives essentially the same sequence, except with the initial 1 replaced by 2.  Thomas Ordowski, Dec 26 2016
The union of 2 and this sequence gives the values k for which 2^k or 2^k  1 are the numbers in A006549.  Gionata Neri, Dec 19 2015


LINKS

Table of n, a(n) for n=1..43.


EXAMPLE

0 is in the sequence because 2^0  1 = 0 is nonprime and 2^0 + 1 = 2 is prime; 2 is not in the sequence because 2^2  1 = 3 and 2^2 + 1 = 5 are both prime.


MATHEMATICA

Select[Range[0, 5000], Xor[PrimeQ[2^#  1], PrimeQ[2^# + 1]] &] (* Michael De Vlieger, Jan 03 2016 *)


PROG

(PARI) isok(n) = my(p = 2^n1, q = p+2); bitxor(isprime(p), isprime(q)); \\ Michel Marcus, Jan 03 2016


CROSSREFS

Cf. A000043, A092506, A019434.
Sequence in context: A266796 A318603 A154571 * A112882 A180152 A162610
Adjacent sequences: A174266 A174267 A174268 * A174270 A174271 A174272


KEYWORD

nonn


AUTHOR

JuriStepan Gerasimov, Mar 14 2010


EXTENSIONS

a(10)a(43) from Charles R Greathouse IV, Mar 20 2010


STATUS

approved



