A261539 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

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

LINKS

Table of n, a(n) for n=1..25.

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

EXAMPLE

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.

MATHEMATICA

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

PROG

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