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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
EXAMPLE
5 is in the sequence because 16^5-4^5-1 = 1047551 is prime.
MATHEMATICA
Select[Range[2500], PrimeQ[16^# - 4^# - 1] &]
PROG
(Magma) [n: n in [0..500] | IsPrime(16^n-4^n-1)];
(PARI) is(n)=ispseudoprime(16^n-4^n-1) \\ Charles R Greathouse IV, Jun 13 2017
CROSSREFS
Cf. A098845, similar sequences listed in A265481.
Sequence in context: A286713 A342013 A213544 * A085410 A073118 A048082
KEYWORD
nonn,more
AUTHOR
Vincenzo Librandi, Dec 10 2015
STATUS
approved

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Last modified May 22 19:06 EDT 2024. Contains 372758 sequences. (Running on oeis4.)