A179077 -id:A179077 - cp's OEIS frontend

A179078 a(n) = ((3^p - 3)/p) mod p where p is n-th prime.

1, 2, 3, 4, 0, 11, 13, 16, 5, 16, 20, 17, 22, 6, 33, 16, 5, 39, 45, 25, 5, 4, 26, 72, 21, 53, 43, 80, 85, 12, 53, 94, 54, 135, 113, 132, 125, 32, 34, 163, 100, 147, 52, 61, 84, 46, 54, 80, 122, 103, 83, 43, 109, 87, 127, 125, 239, 129, 63, 98, 160, 223, 29, 82, 3, 68, 288, 322

Offset: 1

Artur Jasinski, Jun 28 2010

nonn

a(n) = 0 where n=5 (p=11) and n=78940 (p=1006003) see A014127.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A014127, A179077, A377669.

f:= p -> (3&^p-3 mod p^2)/p:
seq(f(ithprime(i)),i=1..100); # Robert Israel, Nov 03 2024

aa = {}; Do[AppendTo[aa, Mod[(3^Prime[n] - 3)/Prime[n], Prime[n]]], {n, 1, 100}]; aa (* Artur Jasinski *)

A377655 a(n) is the least prime p such that (2^p - 2)/p == n (mod p), or -1 if there is no such prime p.

Original entry on oeis.org

1093, 2, 3, 30577, 7, 41, 13, 43, 2633, 17, 11, 23, 31, 83, 233, 103, 59, 97, 25037, 53, 67, 3323, 14717

Offset: 0

Robert Israel, Nov 03 2024

For n = 23, 27, 37, 40, 42, ..., a(n) > 5 * 10^9 if not -1.

a(23) > 2*10^11 if it is not -1. - Michael S. Branicky, Nov 04 2024

			a(4) = 7 because (2^7 - 2)/7 = 18 == 4 (mod 7), and 7 is the first prime that works.

Cf. A179077, A377669.

f:= p -> (2&^p-2 mod p^2)/p:
V:= Array(0..22): 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);

a(n) = prime(i) where A179077(i) = n, if such i exists.

cp's OEIS Frontend

A179078 a(n) = ((3^p - 3)/p) mod p where p is n-th prime.

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