

A357435


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


1



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



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[w1] = 0 then V[w1]:= 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



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



