A101396 Numbers k such that 4*10^k - 9 is prime.

1, 17, 19, 29, 43, 119, 173, 949, 1609, 5579, 19679, 34147, 43493, 97799

Offset: 1

Author

Julien Peter Benney (jpbenney(AT)ftml.net), Jan 15 2005

Keywords

• more
• nonn

Comments

a(15) > 10^5. - Robert Price, Mar 17 2015

All terms are odd, since 4 * 10^(2*k) - 9 = (2 * 10^k - 3)*(2 * 10^k + 3). - Robert Israel, Mar 17 2015

Examples

			n = 1, 17, 19 are members since 31, 399999999999999991 and 39999999999999999991 are primes.
		

Links

• Makoto Kamada, Prime numbers of the form 399...991.
• Index entries for primes involving repunits.

Crossrefs

Cf. A095714, A101848.

Programs

Magma

[n: n in [1..300] |IsPrime(4*10^n - 9)]; // Vincenzo Librandi, Mar 18 2015

Maple

select(n -> n::odd and isprime(4*10^n-9), [$1..10000]); # Robert Israel, Mar 17 2015

Mathematica

Do[ If[ PrimeQ[4*10^n - 9], Print[n]], {n, 0, 10000}]

PARI

is(n)=ispseudoprime(4*10^n-9) \\ Charles R Greathouse IV, Jun 12 2017

Formula

a(n) = A101848(n) + 1.

Extensions

a(11) from Kamada link by Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

a(12)-a(14) from Kamada data by Robert Price, Mar 17 2015