A357435 a(n) is the least prime p such that p^2+4 is a prime times 5^n.

3, 19, 11, 239, 9011, 61511, 75989, 299011, 4517761, 24830261, 666575989, 2541575989, 41989674011, 147951732239, 455568919739, 174807200989, 9513186107239, 215201662669739, 759834958424011, 5581612302174011, 5404715822825989, 112788443850169739, 2606148434986511

Offset

0,1

Comments

a(n) has the form 5^n * k + x, for some k >= 0, where x is a solution to the equation x^2 + 4 == 0 (mod 5^n). - Daniel Suteu, Jan 04 2023

Links

Daniel Suteu, Table of n, a(n) for n = 0..500

Example

a(2) = 11 because 11^2+4 = 125 = 5*5^2, 11 and 5 are prime, and no smaller prime works.
a(3) = 239 because 239^2+4 = 57125 = 457*5^3, 239 and 457 are prime, and no smaller prime works.

Maple

V:= Array(0..11): count:= 0: p:= 1:
while count < 12 do
  p:= nextprime(p);
  v:= p^2+4;
  w:= padic:-ordp(v, 5);
  if v = 5^w and V[w-1] = 0 then V[w-1]:= p; count:= count+1 fi;
  if w <= 11 and V[w] = 0 and isprime(v/5^w) then
     V[w]:= p; count:= count+1
    fi;
od:
convert(V, list);

Mathematica

a[n_] := Module[{p=2, m=5^n}, While[!PrimeQ[Sqrt[p*m - 4]], p = NextPrime[p]]; Sqrt[p*m - 4]]; Array[a, 8, 0] (* Amiram Eldar, Sep 28 2022 *)

Crossrefs

Cf. A357426.

Sequence in context: A145688 A358979 A178985 * A266704 A185446 A172032

Adjacent sequences: A357432 A357433 A357434 * A357436 A357437 A357438

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Sep 28 2022

Extensions

a(12)-a(20) from Giorgos Kalogeropoulos, Sep 28 2022

a(21)-a(22) from Daniel Suteu, Jan 04 2023

Status

approved