A358426 - OEIS

%I #8 Nov 20 2022 18:30:33

%S 3,11,41,359,109,13859,67391,276359,10036141,11057609,511057609,

%T 4528004891,35817391,194860036141,154261057609,1143030588859,

%U 6669469411141,35444788401359,349076695973641,982316442067391,3805192418629891,7047685094411141,190153153844411141,4915609391637379891

%N a(n) is the least prime p such that (p^2 - 6)/5^n is prime.

%H Robert Israel, <a href="/A358426/b358426.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n)^2-6 = 5^n * A358422(n).

%e a(3) = 359 because 359^2 - 6 = 128875 = 5^3 * 1031 where 359 and 1031 are prime, and no smaller prime works.

%p f:= proc(n) local v, a, b, k, p, q;

%p         v:= 5^n;

%p         a:= numtheory:-msqrt(6, v);

%p         if a < v/2 then b:= v-a

%p         else b:= a; a:= v-a

%p         fi;

%p         for k from 0 do

%p           for q in [k*v+a, k*v+b] do

%p             if isprime(q) then

%p               p:= (q^2-6)/v;

%p               if isprime(p) then return q fi;

%p             fi

%p          od od

%p end proc:

%p map(f, [$0..30]);

%Y Cf. A358422.

%K nonn

%O 0,1

%A _J. M. Bergot_ and _Robert Israel_, Nov 15 2022