A358422 a(n) is the least prime p such that 5^n * p + 6 is the square of a prime.

3, 23, 67, 1031, 19, 61463, 290659, 977591, 257853763, 62602607, 26744819683, 419897923439, 5254699, 31105379274647, 3898814282899, 42812012202143, 291516070141267, 1646700822288287, 31943436447743683, 50590939472510999, 151828450171141747, 104165257122907367, 15165857481926132731

Offset

0,1

Links

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

Formula

5^n*a(n) = A358426(n)^2 - 6.

Example

a(3) = 1031 because 5^3 * 1031 + 6 = 128881 = 359^2 where 1031 and 359 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 p fi;
            fi
         od od
end proc:
map(f, [$0..30]);

Crossrefs

Cf. A358426.

Sequence in context: A299311 A300112 A183332 * A196325 A003531 A121984

Adjacent sequences: A358419 A358420 A358421 * A358423 A358424 A358425

Keyword

nonn

Author

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

Status

approved