A281624 Numbers m such that 2^phi(m) + 1 is prime (Fermat prime).

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20, 24, 30, 32, 34, 40, 48, 60

Offset: 1

Author

Jaroslav Krizek, Jan 25 2017

Keywords

• nonn
• more

Comments

Numbers m such that A243305(m) is a Fermat prime (A019434).

If there are only 5 Fermat primes, sequence is finite with 20 terms; corresponding values of Fermat primes: 3, 3, 5, 5, 17, 5, 17, 17, 17, 257, 257, 65537, 257, 257, 257, 65537, 65537, 65537, 65537, 65537.

Number of numbers k such that 2^phi(k) + 1 = A019434(n) for n = 1-5: 2, 3, 4, 5, 6.

Examples

			10 is a term because 2^phi(10) + 1 = 2^4 + 1 = 17 (prime).
		

Crossrefs

Subsequence of A003401.

Cf. A000010 (phi(n)), A019434, A243305, A281623.

Programs

Magma

[n: n in[1..10000] | IsPrime(2^(EulerPhi(n)) + 1)];

Mathematica

Select[Range[60], PrimeQ[2^EulerPhi[#] + 1] &] (* Paolo Xausa, Jan 18 2025 *)

PARI

is(n)=isprime(2^eulerphi(n)+1) \\ Charles R Greathouse IV, Jan 27 2017