A377669 a(n) is the least prime p such that (3^p - 3)/p == n (mod p), or -1 if there is no such prime p.

11, 2, 3, 5, 7, 23, 43, 5721619, 2311, 105830189, 31300663, 13, 113, 17, 821, 1181, 19, 37

Offset: 0

Author

Robert Israel, Nov 03 2024

Keywords

• nonn
• more

Comments

For n = 18, 24, 27, 28, 30, 38, ..., a(n) > 6 * 10^9 if it is not -1.

a(18) > 2*10^11 if it is not -1. - Michael S. Branicky, Nov 04 2024

Examples

			a(4) = 7 because (3^7 - 3)/7 = 312 == 4 (mod 7), and 7 is the first prime that works.
		

Crossrefs

Cf. A179078, A377655.

Programs

Maple

f:= p -> (3&^p-3 mod p^2)/p:
V:= Array(0..17): count:= 0:
p:= 1:
for i from 1 while count < 23 do
  p:= nextprime(p);
  v:= f(p);
  if v <= 22 and V[v] = 0 then V[v]:= i; count:= count+1 fi;
od:
convert(V, list);

Mathematica

lpp[n_]:=Module[{p=2},While[Mod[(3^p-3)/p,p]!=n,p=NextPrime[p]];p]; Array[lpp,17,0] (* Harvey P. Dale, Jun 07 2025 *)

Formula

a(n) = prime(i) where A179078(i) = n, if such i exists.