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A265483 Numbers k such that 25^k - 5^k - 1 is prime. 1
1, 2, 4, 15, 16, 24, 57, 206, 284, 1290, 1722, 1862, 1866, 3271, 5306, 5474, 15401, 18729, 34757, 42842, 63930, 89967 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
For k = 1, 2, 4, 15, 16, the corresponding primes are 19, 599, 389999, 931322574584960937499, 23283064365234374999999.
a(n) is not of the form 5*m + 3 (divisibility by 11) or 9*m + 10 (divisibility by 19), 7*m + (-1)^m + 7 (divisibility by 29) or 29*m + 27 (divisibility by 59).
a(23) > 10^5. - Robert Price, Dec 12 2019
LINKS
EXAMPLE
4 is in the sequence because 25^4-5^4-1 = 389999 is prime.
MATHEMATICA
Select[Range[6000], PrimeQ[25^# - 5^# - 1] &]
PROG
(Magma) [n: n in [0..300] | IsPrime(25^n-5^n-1)];
(PARI) is(n)=ispseudoprime(25^n - 5^n - 1) \\ Anders Hellström, Dec 11 2015
CROSSREFS
Cf. similar sequences listed in A265481.
Sequence in context: A019543 A304568 A271645 * A357692 A154906 A260299
KEYWORD
nonn,more
AUTHOR
Vincenzo Librandi, Dec 11 2015
EXTENSIONS
a(17)-a(22) from Robert Price, Dec 12 2019
STATUS
approved

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Last modified June 21 08:46 EDT 2024. Contains 373543 sequences. (Running on oeis4.)