A261539 Numbers m such that (4^m + 5) / 3 is prime.

0, 1, 2, 3, 6, 9, 12, 21, 42, 150, 195, 390, 411, 1215, 2754, 2757, 3246, 6186, 11340, 12885, 84708, 87120, 191772, 503919, 786441

Offset: 1

Author

Vincenzo Librandi, Aug 25 2015

Keywords

• nonn
• more

Comments

After 1, m is not of the form 3*k+1 because in this case 4^m+5 is divisible by 9; after 2, m is not of the form 3*k+2 because in this case 4^m+5 is divisible by 7. Therefore, m>2 is always a multiple of 3. - Bruno Berselli, Aug 25 2015

Larger members of the sequence generate probable primes only. - Serge Batalov, Aug 27 2015

Examples

			6 is in the sequence because (4^6+5)/3 = 1367 is prime.
9 is in the sequence because (4^9+5)/3 = 87383 is prime.
4 is not in the sequence because (4^4+5)/3 = 87 = 3*29 is not prime.
		

Links

• Henri & Renaud Lifchitz PRPtop, (2^n+5)/3 PRPs

Crossrefs

Cf. A163834.

Cf. numbers n such that (4^n+k)/3 is prime: this sequence (k=5), A261577 (k=11), A261578 (k=17), A261579 (k=23).

Cf. A253772.

Programs

Magma

[n: n in [0..1000] | IsPrime((4^n+5) div 3)];

Mathematica

Select[Range[0, 5000], PrimeQ[(4^# + 5)/3] &]

PARI

isok(n)=isprime((4^n + 5) / 3) \\ Anders Hellström, Aug 25 2015

Extensions

a(18)-a(23) from Lelio R Paula (2012-2014) via Serge Batalov, Aug 27 2015

a(24)-a(25) from Serge Batalov, Aug 29 2015