|
|
A065341
|
|
Mersenne composites: 2^prime(m) - 1 is not a prime.
|
|
20
|
|
|
2047, 8388607, 536870911, 137438953471, 2199023255551, 8796093022207, 140737488355327, 9007199254740991, 576460752303423487, 147573952589676412927, 2361183241434822606847, 9444732965739290427391
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
FORMULA
|
|
|
EXAMPLE
|
2^11 - 1 = 2047 = 23*89.
|
|
MAPLE
|
i := 2^(ithprime(n))-1:
if (not isprime(i)) then
RETURN (i)
|
|
MATHEMATICA
|
Select[Table[2^Prime[n]-1, {n, 30}], !PrimeQ[#]&] (* Harvey P. Dale, May 06 2018 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|