

A048744


Numbers k such that 2^k  k is prime.


13



2, 3, 9, 13, 19, 21, 55, 261, 3415, 4185, 7353, 12213, 44169, 60975, 61011, 108049, 182451, 228271, 481801, 500899, 505431, 1015321, 1061095
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OFFSET

1,1


COMMENTS

All terms except for the first are odd.  Joerg Arndt, Jul 19 2016
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



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: *)


PROG

(PARI)
for(n=1, 10^5, if(ispseudoprime(2^nn), print1(n, ", "))) \\ Derek Orr, Sep 01 2014


CROSSREFS



KEYWORD

nonn,nice,hard,more


AUTHOR



EXTENSIONS

4185 and 7353 are probable primes (the latter was found by Jud McCranie).
More terms from Henri Lifchitz contributed by Ray Chandler, Mar 02 2007


STATUS

approved



