A101398 Numbers k such that 4*10^k-3 is prime.

1, 2, 14, 20, 30, 44, 66, 260, 872, 8846, 26744, 57506, 98472, 106892

Offset: 1

Author

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

Keywords

• nonn
• more

Comments

See Kamada link for search limit and prime vs. PRP status.

a(14) > 10^5. - Robert Price, Mar 17 2015

a(15) > 2*10^5. - Robert Price, Oct 02 2015

Examples

			k = 1, 2, 14, 20 are members since 37, 397, 399999999999997 and 399999999999999999997
are prime numbers.
		

Links

• Makoto Kamada, Prime numbers of the form 399...997.
• Index entries for primes involving repunits.

Crossrefs

Cf. A089675, A101849.

Programs

Mathematica

Do[ If[ PrimeQ[4*10^n - 3], Print[n]], {n, 0, 10000}]

PARI

for(n=1, 1e4, if(isprime(4*10^n-3), print1(n", "))) \\ Altug Alkan, Oct 02 2015

Formula

a(n) = A101849(n) + 1.

Extensions

a(11)-a(12) from Kamada data by Robert Price, Dec 13 2010

a(13) from Kamada data by Robert Price, Mar 17 2015

a(14) from Robert Price, Oct 02 2015