A269835 Primes p of the form 2^k + 4*(-1)^k - 3.

2, 5, 17, 257, 65537, 549755813881

Offset: 1

Author

Jaroslav Krizek, Mar 06 2016

Keywords

• nonn

Comments

a(7) has 216 digits (see b-file).

Fermat primes > 3 from A019434 are terms.

Corresponding values of k: 0, 2, 4, 8, 16, 39, 715, ....

Note that for k = 1, 2^k + 4*(-1)^k - 3 = -5.

For further k values, see A059609. (2^k-7 is divisible by 3 for even k.) - Jeppe Stig Nielsen, Nov 18 2019

Links

• Jeppe Stig Nielsen, Table of n, a(n) for n = 1..10 (terms 1..7 from Jaroslav Krizek).

Crossrefs

Cf. A019434, A059609.

Programs

Magma

[2] cat [2^k + 4*(-1)^k - 3: k in [2..300] | IsPrime(2^k + 4*(-1)^k - 3)];

Mathematica

Select[Table[2^k+4(-1)^k-3,{k,0,50}],Positive[#]&&PrimeQ[#]&] (* Harvey P. Dale, Sep 14 2019 *)

PARI

for (k=0,40,my(j=2^k+4*(-1)^k-3);if(isprime(j),print1(j,", "))) \\ Hugo Pfoertner, Nov 21 2019