OFFSET
1,1
COMMENTS
All terms except for the first are odd. - Joerg Arndt, Jul 19 2016
From Iain Fox, Nov 14 2017: (Start)
If k is congruent to 5 mod 6, then 3 divides 2^k - k; therefore a(n) is never congruent to 5 mod 6.
For even k, 2^k - k is divisible by 2; thus all terms other than 2 are odd.
It follows that for n > 1, a(n) is congruent to {1, 3} mod 6.
(End)
REFERENCES
J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 261, p. 70, Ellipses, Paris 2008.
LINKS
Henri Lifchitz, Renaud Lifchitz, PRP Top Records. 2^n-n.
EXAMPLE
2^55 - 55 = 36028797018963913 is prime, so 55 is a term.
MATHEMATICA
Do[ If[ PrimeQ[ 2^n - n ], Print[ n ] ], {n, 0, 7353} ]
(* Second program: *)
Select[Range[8000], PrimeQ[2^# - #] &] (* Michael De Vlieger, Nov 15 2017 *)
PROG
(PARI)
for(n=1, 10^5, if(ispseudoprime(2^n-n), print1(n, ", "))) \\ Derek Orr, Sep 01 2014
CROSSREFS
KEYWORD
nonn,nice,hard,more
AUTHOR
EXTENSIONS
261 and 3415 found by Warut Roonguthai
4185 and 7353 are probable primes (the latter was found by Jud McCranie).
12213 found by Robert G. Wilson v, Jan 02 2001
More terms from Henri Lifchitz contributed by Ray Chandler, Mar 02 2007
Edited by T. D. Noe, Oct 30 2008
a(22)-a(23) from Henri Lifchitz contributed by Robert Price, Sep 01 2014
STATUS
approved