A130061 Numbers k that divide 3^((k-1)/2) - 2^((k-1)/2) - 1.

1, 3, 35, 147, 195, 219, 291, 399, 579, 583, 723, 939, 1011, 1023, 1227, 1299, 1371, 1443, 1731, 1803, 2019, 2307, 2499, 2811, 3003, 3027, 3099, 3387, 3459, 3603, 3747, 3891, 3963, 4467, 4623, 4827, 4971, 5187, 5259, 5331, 5403, 5619, 5979, 6051, 6267

Offset: 1

Author

Alexander Adamchuk, May 05 2007

Keywords

• nonn

Comments

It appears that all terms are composite except a(1) = 1 and a(2) = 3. Most listed terms are divisible by 3, except {1, 35, 583, 70643, ...}.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A097934 (primes p that divide 3^((p-1)/2) - 2^((p-1)/2)).

Cf. A038876 (primes p such that 6 is a square mod p).

Cf. A127071, A127072, A127073, A127074.

Cf. A130058, A130059, A130060, A130062, A130063.

Programs

Mathematica

Select[ Range[10000], Mod[ PowerMod[3,(#-1)/2,# ] - PowerMod[2,(#-1)/2,# ] -1, # ]==0&]