A057733 Primes of the form 2^k + 3.
5, 7, 11, 19, 67, 131, 4099, 32771, 65539, 262147, 268435459, 1073741827, 36028797018963971, 147573952589676412931, 19342813113834066795298819, 431359146674410236714672241392314090778194310760649159697657763987459
Offset: 1
Keywords
Links
- Robert Israel, Table of n, a(n) for n = 1..25
- Christian Kassel and Christophe Reutenauer, Pairs of intertwined integer sequences, arXiv:2507.15780 [math.NT], 2025. See p. 12.
Programs
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Magma
[ a: n in [0..250] | IsPrime(a) where a is 2^n+3 ] // Vincenzo Librandi, Aug 07 2010
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Maple
for n from 1 to 2000 do `if`(isprime(2^n + 3), 2^n + 3, NULL) od; # alternative: select(isprime, [seq(2^n+3,n=1..2000)]); # Robert Israel, Dec 28 2015
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Mathematica
Select[Table[2^n + 3, {n, 230}], PrimeQ] (* Jayanta Basu, May 23 2013 *) -
PARI
for(n=1,99,if(ispseudoprime(t=2^n+3),print1(t", "))) \\ Charles R Greathouse IV, Jul 02 2013
Formula
a(n) = 2^A057732(n) + 3. - Elmo R. Oliveira, Nov 08 2023
Extensions
More terms from Francois Jooste (pin(AT)myway.com), Mar 17 2003