A317887 Numbers k such that 4^k - 3^k + 2^k is prime.

1, 2, 4, 18, 56, 60, 88, 1288, 1784, 3406, 9250, 11968, 36216, 57206, 89148, 107514, 155410, 202906

Offset: 1

Author

Jinyuan Wang, Aug 09 2018

Keywords

• nonn
• more

Comments

1 is the only odd number in this sequence.

a(15) > 65432.

a(16) > 10^5. - Michael S. Branicky, Nov 21 2024

Examples

			2 is in the sequence since 4^2 - 3^2 + 2^2 = 16 - 9 + 4 = 11 is prime.
		

Crossrefs

Cf. A083324, A138699.

Programs

Mathematica

Select[Range[0, 5000], PrimeQ[4^# - 3^# + 2^#] &]

PARI

for(n=1, 5000, if(ispseudoprime(4^n-3^n+2^n), print1(n, ", ")))

Extensions

a(13)-a(14) from Giovanni Resta, Aug 10 2018

a(15) from Michael S. Branicky, Nov 21 2024

a(16) from Georg Grasegger, Apr 07 2025

a(17)-a(18) from Georg Grasegger, May 06 2025