A120375 Integers k such that 2*5^k - 1 is prime.

4, 6, 16, 24, 30, 54, 96, 178, 274, 1332, 2766, 3060, 4204, 17736, 190062, 223536, 260400, 683080

Offset: 1

Author

Walter Kehowski, Jun 28 2006

Keywords

• nonn
• more

Comments

See comments for A057472. Examined in base 12, all n must be even and all primes must be 1-primes. For example, 1249 is 881 in base 12.

a(16) > 2*10^5. - Robert Price, Mar 14 2015

Examples

			a(1) = 4 since 2*5^4 - 1 = 1249 is the first prime.
		

Crossrefs

Integers k such that 2*b^k - 1 is prime: A090748 (b=2), A003307 (b=3), this sequence (b=5), A057472 (b=6), A002959 (b=7), A002957 (b=10), A120378 (b=11).

Primes of the form 2*b^k - 1: A000668 (b=2), A079363 (b=3), A120376 (b=5), A158795 (b=7), A055558 (b=10), A120377 (b=11).

Cf. also A000043, A002958.

Programs

Magma

[n: n in [0..2800] |IsPrime(2*5^n - 1)]; // Vincenzo Librandi, Sep 23 2018

Maple

for w to 1 do for k from 1 to 2000 do n:=2*5^k-1; if isprime(n) then printf("%d, %d ",k,n) fi od od;

Mathematica

Select[Range[0, 100], PrimeQ[2*5^# - 1] &] (* Robert Price, Mar 14 2015 *)

PARI

isok(k) = ispseudoprime(2*5^k-1); \\ Altug Alkan, Sep 22 2018

Formula

a(n) = 2*A002958(n).

Extensions

More terms from Ryan Propper, Mar 28 2007

a(14) from Herman Jamke (hermanjamke(AT)fastmail.fm), May 02 2007

a(15) from Robert Price, Mar 14 2015

a(16)-a(18) from Jorge Coveiro and Tyler NeSmith, Jun 14 2020