A261577 Numbers m such that (4^m + 11) / 3 is prime.

1, 4, 10, 34, 40, 106, 418, 682, 12702, 30484, 182026, 217720, 241306

Offset: 1

Author

Vincenzo Librandi, Aug 26 2015

Keywords

• nonn
• more

Comments

From Bruno Berselli, Aug 26 2015: (Start)

After 1, m is always even (for m odd 4^m+11 is divisible by 5).

Let m = 2*h. For h = 3*k+1, 9*k+3, 11*k+2, 11*k+8, 13*k+8, 19*k+6, 23*k+10, 23*k+14 and 29*k+28, 4^m+11 is divisible by 9, 37, 89, 23, 53, 229, 47, 1013 and 59, respectively. (End)

All terms appear to be of the form 3*k+1. - Dhilan Lahoti, Aug 31 2015

12702 is the first counterexample to Dhilan Lahoti's conjecture: 12702 = 3*4234. - Bruno Berselli, Feb 02 2017

a(14) > 300,000. - Robert Price, Mar 18 2017

Examples

			4 is in the sequence because (4^4+11)/3 = 89 is prime.
10 is in the sequence because (4^10+11)/3 = 349529 is prime.
		

Crossrefs

Cf. A163868.

Cf. similar sequences listed in A261539.

Programs

Magma

[n: n in [0..1500] | IsPrime((4^n+11) div 3)];

Mathematica

Select[Range[0, 5000], PrimeQ[(4^# + 11)/3] &]

PARI

is(n)=isprime((4^n + 11) / 3) \\ Anders Hellström, Aug 31 2015

Extensions

a(9)-a(12) from Robert Price, Feb 01 2017

a(13) from Robert Price, Mar 18 2017