A005539 Numbers k such that 10*3^k + 1 is prime.

0, 1, 3, 4, 7, 9, 12, 18, 22, 102, 112, 157, 162, 289, 619, 763, 1389, 1783, 1882, 3294, 3567, 13297, 14932, 18954, 19612, 23598, 33882, 66874, 70546, 86568, 187626, 190738

Offset: 1

Author

N. J. A. Sloane

Keywords

• hard
• nonn

Comments

a(33) > 2*10^5. - Robert Price, Mar 16 2014

All terms are verified primes (i.e., not merely probable primes). - Robert Price, Mar 16 2014

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• H. C. Williams and C. R. Zarnke, Some prime numbers of the forms 2*3^n+1 and 2*3^n-1, Math. Comp., 26 (1972), 995-998.

Programs

Magma

[n: n in [0..3567] | IsPrime(10*3^n + 1) ]; // Vincenzo Librandi, Sep 26 2012

Mathematica

Do[ If[ PrimeQ[ 10*3^n + 1], Print[n]], {n, 0, 6810}]

PARI

is(n)=ispseudoprime(10*3^n+1) \\ Charles R Greathouse IV, Feb 20 2017

Extensions

More terms from Robert G. Wilson v, Sep 07 2000

a(1)=0 added and typo in Mathematica program fixed by Vincenzo Librandi, Sep 26 2012

a(22)-a(32) from Robert Price, Mar 16 2014