A358426 a(n) is the least prime p such that (p^2 - 6)/5^n is prime.

3, 11, 41, 359, 109, 13859, 67391, 276359, 10036141, 11057609, 511057609, 4528004891, 35817391, 194860036141, 154261057609, 1143030588859, 6669469411141, 35444788401359, 349076695973641, 982316442067391, 3805192418629891, 7047685094411141, 190153153844411141, 4915609391637379891

Offset

0,1

Links

Robert Israel, Table of n, a(n) for n = 0..1000

Formula

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

Example

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

Maple

f:= proc(n) local v, a, b, k, p, q;
        v:= 5^n;
        a:= numtheory:-msqrt(6, v);
        if a < v/2 then b:= v-a
        else b:= a; a:= v-a
        fi;
        for k from 0 do
          for q in [k*v+a, k*v+b] do
            if isprime(q) then
              p:= (q^2-6)/v;
              if isprime(p) then return q fi;
            fi
         od od
end proc:
map(f, [$0..30]);

Crossrefs

Cf. A358422.

Sequence in context: A149067 A018962 A102417 * A096147 A225431 A359248

Adjacent sequences: A358423 A358424 A358425 * A358427 A358428 A358429

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Nov 15 2022

Status

approved