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
Keywords
Examples
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.
Links
- Daniel Suteu, Table of n, a(n) for n = 0..500
Crossrefs
Cf. A357426.
Programs
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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 *)
Extensions
a(12)-a(20) from Giorgos Kalogeropoulos, Sep 28 2022
a(21)-a(22) from Daniel Suteu, Jan 04 2023
Comments