A320282 a(n) = (3^(prime(n)-1) - 2^(prime(n)-1))/prime(n).

13, 95, 5275, 40565, 2528305, 20376755, 1364211535, 788845655845, 6641614785575, 4056609907500605, 296528399013300025, 2544627551941066235, 188573149984760785495, 121907205372133465501165, 79832689778949397606269355, 694937020886283311634222725, 461241110187445155009340352195

Offset: 3

Author

Jianing Song, Oct 09 2018

Keywords

• nonn

Comments

Fermat quotients in base 3/2.

For n > 3, a(n) is divisible by 5.

Primes p such that p^2 divides 3^(p-1) - 2^(p-1) (base-3/2 Wieferich primes) are p = 23, ... What's the next?

Examples

			For n = 3, prime(3) = 5 and a(3) = (3^4 - 2^4)/5 = 13.
For n = 4, prime(4) = 7 and a(4) = (3^6 - 2^6)/7 = 95.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 3..317

Crossrefs

Cf. A073631 (base-3/2 Fermat pseudoprimes).

Programs

Magma

[(3^(p-1) - 2^(p-1))  div p: p in PrimesInInterval(4, 100)]; // Vincenzo Librandi, Oct 12 2018

Mathematica

p[n_]:=Prime[n]; a[n_]:=(3^(p[n]-1) - 2^(p[n]-1))/p[n]; Array[a, 50, 3] (* Stefano Spezia, Oct 11 2018 *)

PARI

a(n) = my(p=prime(n)); (3^(p-1) - 2^(p-1))/p