A130062 Nonprime numbers k such that k divides 3^((k+1)/2) - 2^((k+1)/2) - 1.

1, 21, 49, 105, 1729, 2465, 2877, 7305, 10585, 15841, 31021, 31621, 32041, 41041, 46657, 52633, 54145, 75361, 83333, 115921, 126217, 162401, 172081, 211141, 282133, 284649, 294409, 334153, 383161, 399001, 417241, 449065, 488881, 530881

Offset: 1

Author

Alexander Adamchuk, May 05 2007

Keywords

• nonn

Comments

The perfect squares in listed terms are a(1) = 1, a(3) = 49 = 7^2, a(13) = 32041 = 179^2 and a(29) = 383161 = 619^2.

Note that primes {7,179,619} are the terms of A130060 or primes in A127074.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

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, A130061, A130063, A130060, A127074.

Programs

Mathematica

Select[ 2*Range[100000]-1, !PrimeQ[ # ] && Mod[ PowerMod[3,(#+1)/2,# ] - PowerMod[2,(#+1)/2,# ] - 1, # ] == 0 & ]

Extensions

More terms from Ryan Propper, Jan 07 2008