A120376 - OEIS

%I #20 Jun 21 2020 01:55:25

%S 1249,31249,305175781249,119209289550781249,1862645149230957031249,

%T 111022302462515654042363166809082031249,

%U 25243548967072377773175314089049159349542605923488736152648925781249

%N Primes of the form 2*5^k - 1.

%C 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.

%C The next term has 125 digits. - _Harvey P. Dale_, Jan 26 2019

%F a(n) = 2*5^A120375(n) - 1 = 2*5^(2*A002958(n)) - 1. - _Jianing Song_, Sep 22 2018

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

%p 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;

%t Select[2*5^Range[100]-1,PrimeQ] (* _Harvey P. Dale_, Jan 26 2019 *)

%o (PARI) for(k=1, 1e3, if(ispseudoprime(p=2*5^k-1), print1(p, ", "))); \\ _Altug Alkan_, Sep 22 2018

%Y Integers k such that 2*b^k - 1 is prime: A090748 (b=2), A003307 (b=3), A120375 (b=5), A057472 (b=6), A002959 (b=7), A002957 (b=10), A120378 (b=11).

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

%Y Cf. also A000043, A002958.

%K nonn

%O 1,1

%A _Walter Kehowski_, Jun 28 2006