A329309 - OEIS

%I #24 Sep 08 2022 08:46:24

%S 2,7,11,23,43,67,83,173,167,227,367,331,503,607,727,827,1031,1447,

%T 1223,1163,1523,1973,2957,2357,1811,3083,3631,3607,4423,5419,6779,

%U 5297,6353,7207,7307,7817,9803,6563,8861,8123,10223,10883,13331,10853,14423,14419,17597,15307,15083,15889,21227,19403

%N a(n) is the first prime p such that A329308(p) = n.

%H Robert Israel, <a href="/A329309/b329309.txt">Table of n, a(n) for n = 0..325</a>

%e a(3)=23 because A329308(23)=3 and 23 is the least prime with this property.

%p f:= proc(n) local k; nops(select(isprime, [seq(n mod k^2, k=2..floor(sqrt(n)))])) end proc:

%p V:= Array(0..100): count:= 0: p:= 0:

%p while count < 101 do

%p p:= nextprime(p);

%p v:= f(p);

%p if v <= 100 and V[v]=0 then

%p   count:= count+1; V[v]:= p;

%p fi

%p od:

%p convert(V,list);

%t b[n_] := b[n] = (* A329309 *) Select[Range[2, Sqrt[n] // Floor], PrimeQ[ Mod[n, #^2]]&] // Length;

%t a[n_] := For[p = 2, True, p = NextPrime[p], If[b[p] == n, Print[n, " ", p]; Return[p]]];

%t a /@ Range[0, 100] (* _Jean-François Alcover_, Aug 22 2020 *)

%o (Magma) a:=[]; for n in [0..50] do p:=2; while #[ k:k in [2..Floor(Sqrt(p))]| IsPrime(p mod k^2) ] ne n do p:=NextPrime(p); end while; Append(~a,p); end for; a; // _Marius A. Burtea_, Nov 11 2019

%Y Cf. A329308.

%K nonn

%O 0,1

%A _J. M. Bergot_ and _Robert Israel_, Nov 09 2019