A248613 Numbers n such that (4 * 6^n + 1)/5 is prime.

1, 2, 3, 5, 15, 25, 29, 73, 90, 139, 194, 242, 939, 3518, 3963, 4694, 5570, 5615, 6702, 13962, 14269, 16339, 16882, 22582, 31415, 105554, 120749

Offset

1,2

Comments

Also numbers n such that the generalized near-repunit 444...445 (in base 6) of length n is prime.

Numbers corresponding to a(n) > 3963 are only strong probable primes; smaller ones were proved with Primo-4.0.5.

Note that there are no multiples of 4 in this sequence. That's because if n = 4m, then (4 * 6^n + 1)/5 = (2 * 6^(2m) + 2 * 6^m + 1)/5 * (2 * 6^(2m) - 2*6^m + 1).

Links

Table of n, a(n) for n=1..27.

Eric Weisstein's World of Mathematics, Repunit.

Decimal near-repunit prime sequences.

Example

For n = 5, a(5) = 15 because (4 * 6^15 + 1)/5 = 376147987661 is prime. (In base 6, that is 444444444444445.)

Maple

A248613:=n->`if`(isprime((4*6^n+1)/5), n, NULL): seq(A248613(n), n=1..10^3); # Wesley Ivan Hurt, Oct 09 2014

Mathematica

Select[Range[1000], PrimeQ[(4 * 6^# + 1)/5] &]

Prog

(PARI)
for(n=1, 22582, if(n%4>0 && ispseudoprime((4*6^n+1)/5), print1(n, ", ")));
\\ if n % 4 == 0, no primes due to Aurifeuillean factorization
(Magma) [n: n in [0..300] | IsPrime((4*6^n+1) div 5)]; // Vincenzo Librandi, Oct 17 2014

Crossrefs

Sequence in context: A072246 A292903 A296051 * A024781 A340643 A120755

Adjacent sequences: A248610 A248611 A248612 * A248614 A248615 A248616

Keyword

nonn,more

Author

Serge Batalov, Oct 09 2014

Status

approved