|
| |
|
|
A174269
|
|
Numbers k such that exactly one of 2^k - 1 and 2^k + 1 is a prime.
|
|
4
|
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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 k such that one of 2^k+1 or 2^k-1 is prime, but not both. - R. J. Mathar, Mar 29 2010
The sequence "Numbers k such that 2^k + (-1)^k 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
The union of 2 and this sequence is the values k for which either 2^k - 1 or 2^k + 1, or both, are prime. The reason why this only yields one additional term, 2, is because the number 3 always divides either 2^k - 1 or 2^k + 1 (also implicit in Ordowski comment). - Jeppe Stig Nielsen, Feb 19 2023
|
|
|
LINKS
|
|
|
|
FORMULA
|
|
|
|
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(k) = my(p = 2^k-1, q = p+2); bitxor(isprime(p), isprime(q)); \\ Michel Marcus, Jan 03 2016
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
|
