A129517 Odd primes p such that p divides (p-1)!!-1.

11, 19, 23, 31, 43, 67, 71, 131, 151, 163, 167, 179, 223, 227, 239, 271, 311, 347, 359, 419, 439, 443, 463, 487, 491, 523, 563, 571, 619, 647, 683, 691, 719, 739, 751, 787, 911, 919, 947, 967, 983, 1019, 1031, 1039, 1051, 1063, 1091, 1103, 1123, 1187, 1223

Offset: 1

Author

Alexander Adamchuk, Apr 18 2007

Keywords

• nonn

Comments

All terms are primes of the form 4k+3 (A002145). A002145 is the union of {a(n)} and A129518 (numbers k > 2 such that k divides (k-2)!!-1 and (k-3)!!-1).

Primes such that ((p-1)/2)! = (-1)^((p^2-1)/8) in the finite field F_p of p elements. For example, 11 is a term since ((11-1)/2)! = 5! = -1 = (-1)^((121-1)/8) in F_11. - Luis H. Gallardo, Dec 30 2021

Links

• Jon E. Schoenfield, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006882, A002145, A129518, A129516.

Programs

Mathematica

Select[Prime@Range[2,200],Mod[(#-1)!!-1,#]==0&] (* Giorgos Kalogeropoulos, Jan 09 2022 *)