

A265481


Numbers k such that 9^k  3^k  1 is prime.


9



1, 2, 3, 6, 7, 20, 35, 36, 140, 523, 1170, 1731, 1842, 3727, 3886, 9270, 11071, 13823, 14451, 27086, 27606, 31876, 78008
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OFFSET

1,2


COMMENTS

For k = 1, 2, 3, 6, 7, 20, 35, the corresponding primes are 5, 71, 701, 530711, 4780781, 12157665455570144399, 2503155504993241551284026887086141.
a(n) is not of the form 4*k+5 (divisibility by 5) or 5*k+4 (divisibility by 11) or 9*k+4*(1)^k (divisibility by 19).
Conjectures: a(n) is not of the form 7*k+4 or 8*k.
a(17) = 11071 mod 7 is 4, so the first half of the conjecture above is not true.  Robert Price, Sep 25 2019
a(23) = 78008 is divisible by 8, so the second half of the conjecture above is not true.  Robert Price, Sep 25 2019


LINKS



EXAMPLE

6 is in the sequence because 9^6  3^6  1 = 530711 is prime.


MATHEMATICA

Select[Range[1500], PrimeQ[9^#  3^#  1] &]


PROG

(Magma) [n: n in [0..500]  IsPrime(9^n3^n1)];


CROSSREFS



KEYWORD

nonn,more


AUTHOR



EXTENSIONS



STATUS

approved



