A128027 Numbers n such that (11^n - 3^n)/8 is prime.

3, 5, 19, 31, 367, 389, 431, 2179, 10667, 13103, 90397

Offset: 1

Author

Alexander Adamchuk, Feb 11 2007

Keywords

• hard
• more
• nonn

Comments

All terms are primes.

No other terms < 10^5.

Crossrefs

Cf. A028491 = numbers n such that (3^n - 1)/2 is prime. Cf. A057468 = numbers n such that 3^n - 2^n is prime. Cf. A059801 = numbers n such that 4^n - 3^n is prime. Cf. A121877 = numbers n such that (5^n - 3^n)/2 is a prime. Cf. A128024, A128025, A128026, A128028, A128029, A128030, A128031, A128032.

Programs

Magma

[p: p in PrimesUpTo(400) | IsPrime((11^p-3^p) div 8)]; // Vincenzo Librandi, Nov 20 2014

Maple

A128027:=n->`if`(isprime((11^n-3^n)/8),n,NULL): seq(A128027(n),n=1..1000); # Wesley Ivan Hurt, Nov 19 2014

Mathematica

k=8; Select[ Prime[ Range[1,200] ], PrimeQ[ ((k+3)^# - 3^#)/k ]& ]
Do[If[PrimeQ[(11^n - 3^n)/8], Print[n]], {n, 10^4}] (* Ryan Propper, Mar 17 2007 *)
Select[Prime[Range[1200]], PrimeQ[(11^# - 3^#)/8] &] (* Vincenzo Librandi, Nov 20 2014 *)

PARI

is(n)=ispseudoprime((11^n - 3^n)/8) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(8) from Ryan Propper, Mar 17 2007

a(9) from Farideh Firoozbakht, Apr 04 2007

a(10)=13103, a(11)=90397 from Robert Price, Apr 24 2011