

A261539


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


4



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
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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)];
(PARI) isok(n)=isprime((4^n + 5) / 3) \\ Anders HellstrÃ¶m, Aug 25 2015


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.
Sequence in context: A309677 A058616 A298435 * A325552 A271882 A123316
Adjacent sequences: A261536 A261537 A261538 * A261540 A261541 A261542


KEYWORD

nonn,more


AUTHOR

Vincenzo Librandi, Aug 25 2015


EXTENSIONS

a(18)a(23) from Lelio R Paula (20122014) via Serge Batalov, Aug 27 2015
a(24)a(25) from Serge Batalov, Aug 29 2015


STATUS

approved



