

A265482


Numbers n such that 16^n  4^n  1 is prime.


1



1, 2, 5, 9, 19, 25, 54, 104, 112, 120, 177, 317, 504, 540, 734, 780, 1649, 1923, 2715, 4308, 5917, 6494, 7305, 22653, 26888, 71448, 93834, 137027, 158472, 174648
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

For n = 1, 2, 5, 9, 19, 25, the corresponding primes are 11, 239, 1047551, 68719214591, 75557863725639445512191, 1267650600228228275596796362751.
a(n) is not of the form 5*k+6 (divisibility by 11) or 9*k+8 (divisibility by 19) or 7*k+3*(1)^k (divisibility by 29).
Conjecture: the odd terms are not of the form 8*k+7.
n is in the sequence iff 2*n is in A098845 (terms a(21)a(30) are derived from that sequence).  Ray Chandler, Sep 25 2019


LINKS

Table of n, a(n) for n=1..30.


EXAMPLE

5 is in the sequence because 16^54^51 = 1047551 is prime.


MATHEMATICA

Select[Range[2500], PrimeQ[16^#  4^#  1] &]


PROG

(MAGMA) [n: n in [0..500]  IsPrime(16^n4^n1)];
(PARI) is(n)=ispseudoprime(16^n4^n1) \\ Charles R Greathouse IV, Jun 13 2017


CROSSREFS

Cf. A098845, similar sequences listed in A265481.
Sequence in context: A152546 A286713 A213544 * A085410 A073118 A048082
Adjacent sequences: A265479 A265480 A265481 * A265483 A265484 A265485


KEYWORD

nonn,more


AUTHOR

Vincenzo Librandi, Dec 10 2015


STATUS

approved



