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A065341
Mersenne composites: 2^prime(m) - 1 is not a prime.
20
2047, 8388607, 536870911, 137438953471, 2199023255551, 8796093022207, 140737488355327, 9007199254740991, 576460752303423487, 147573952589676412927, 2361183241434822606847, 9444732965739290427391
OFFSET
1,1
COMMENTS
For the number of prime factors in a(n) see A135975. For indices of primes n in composite 2^prime(n)-1 see A135980. For smallest prime divisors of Mersenne composites see A136030. For largest prime divisors of Mersenne composites see A136031. For largest divisors see A145097. - Artur Jasinski, Oct 01 2008
All the terms are Fermat pseudoprimes to base 2 (A001567). For a proof see, e.g., Jaroma and Reddy (2007). - Amiram Eldar, Jul 24 2021
LINKS
John H. Jaroma and Kamaliya N. Reddy, Classical and alternative approaches to the Mersenne and Fermat numbers, The American Mathematical Monthly, Vol. 114, No. 8 (2007), pp. 677-687.
FORMULA
a(n) = 2^A054723(n) - 1.
EXAMPLE
2^11 - 1 = 2047 = 23*89.
MAPLE
A065341 := proc(n) local i;
i := 2^(ithprime(n))-1:
if (not isprime(i)) then
RETURN (i)
fi: end: seq(A065341(n), n=1..21); # Jani Melik, Feb 09 2011
MATHEMATICA
Select[Table[2^Prime[n]-1, {n, 30}], !PrimeQ[#]&] (* Harvey P. Dale, May 06 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Oct 30 2001
STATUS
approved