A130063 Primes p such that p divides 3^((p+1)/2) - 2^((p+1)/2) - 1.

23, 47, 71, 73, 97, 167, 191, 193, 239, 241, 263, 311, 313, 337, 359, 383, 409, 431, 433, 457, 479, 503, 577, 599, 601, 647, 673, 719, 743, 769, 839, 863, 887, 911, 937, 983, 1009, 1031, 1033, 1103, 1129, 1151, 1153, 1201, 1223, 1249, 1297, 1319, 1321, 1367

Offset: 1

Author

Alexander Adamchuk, May 05 2007

Keywords

• nonn
• easy

Comments

Primes = 1 or 23 mod 24. Hence, together with 2, primes such that (2/p) = 1 = (3/p) where (k/p) is the Legendre symbol. - Charles R Greathouse IV, Apr 06 2012

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A097934 = Primes p such that p divides 3^((p-1)/2) - 2^((p-1)/2).

Subsequence of A038876.

Cf. A127071, A127072, A127073, A127074. Cf. A130058, A130059, A130060, A130061, A130062.

Programs

Mathematica

Select[ Range[2000], PrimeQ[ # ]&&Mod[ PowerMod[3,(#+1)/2,# ] - PowerMod[2,(#+1)/2,# ] - 1, # ]==0&]
Select[Prime[Range[250]],Divisible[3^((#+1)/2)-2^((#+1)/2)-1,#]&] (* Harvey P. Dale, Mar 21 2021 *)

PARI

is(n)=(n+1)%24<3 && isprime(n) \\ Charles R Greathouse IV, Apr 06 2012