A130060 Primes p such that p^2 divides 3^p - 2^p - 1; or primes in A127074(n).

2, 3, 7, 179, 619, 17807

Offset: 1

Author

Alexander Adamchuk, May 05 2007

Keywords

• hard
• more
• nonn

Comments

The prime p divides 3^p - 2^p - 1. Quotients (3^p - 2^p - 1)/p, where p = Prime[n], are listed in A127071. - Alexander Adamchuk, Jan 31 2008

a(7) > 10^9. [From D. S. McNeil, Mar 16 2009]

Crossrefs

Cf. A127071, A127072, A127073, A127074 = numbers n such that n^2 divides 3^n - 2^n - 1. Cf. A130058, A130059, A130061, A130062, A130063.

Programs

Mathematica

Do[ n=Prime[k]; f=PowerMod[3,n,n^2] - PowerMod[2,n,n^2] - 1; If[ IntegerQ[ f/n^2 ], Print[n] ], {k,1,100000} ]

Extensions

2 more terms found by Ryan Propper, Jan 01 2008.

Incorrect a(7), a(8) removed by D. S. McNeil, Mar 16 2009. (The old version was 2,3,7,179,619,17807,135433,1376257.)