A046865 Numbers k such that 4*5^k - 1 is prime.

0, 1, 3, 9, 13, 15, 25, 39, 69, 165, 171, 209, 339, 2033, 6583, 15393, 282989, 498483, 504221, 754611, 864751

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• hard
• nice
• more

Comments

a(22) > 1000000. - Karsten Bonath, Apr 04 2019

References

• R. K. Guy, Unsolved Problems in Number Theory, Section A3.

Links

• Steven Harvey, Williams Primes
• H. C. Williams, The primality of certain integers of the form 2Ar^n - 1, Acta Arith. 39 (1981), 7-17.

Crossrefs

Cf. A003307, A002235, A079906, A046866, A001771, A005541, A056725, A046867, A079907.

Programs

Mathematica

Print[0]; Do[ If[ PrimeQ[4*5^n - 1], Print[n]], {n, 1, 8100, 2}]

PARI

is(n)=isprime(4*5^n-1) \\ Charles R Greathouse IV, Feb 07 2017

Extensions

Two more terms from Robert G. Wilson v, Jan 16 2003 and Jan 26 2003

a(16) from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 05 2008

a(1)=0 prepended by Robert Price, Feb 27 2015

a(17) from Karsten Bonath, Dec 07 2018

a(18)-a(19) from Karsten Bonath, Jan 17 2019

a(20)-a(21) from Karsten Bonath, Apr 04 2019