A129516 -id:A129516 - cp's OEIS frontend

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

Alexander Adamchuk, Apr 18 2007

nonn

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

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

Cf. A006882, A002145, A129518, A129516.

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

A129518 Numbers k > 2 such that k divides (k-2)!! - 1 and (k-3)!! - 1.

Original entry on oeis.org

3, 7, 47, 59, 79, 83, 103, 107, 127, 139, 191, 199, 211, 251, 263, 283, 307, 331, 367, 379, 383, 431, 467, 479, 499, 503, 547, 587, 599, 607, 631, 643, 659, 727, 743, 811, 823, 827, 839, 859, 863, 883, 887, 907, 971, 991, 1087, 1151, 1163, 1171, 1259, 1283

Offset: 1

Alexander Adamchuk, Apr 18 2007

nonn

All terms are primes of the form 4m+3 belonging to A002145. A002145 is the union of this sequence and A129517 (odd primes p such that p divides (p-1)!! - 1).

Odd numbers k > 1 such that k divides (k-1)!! + 1. - Thomas Ordowski, Jul 26 2016

Cf. A006882 (double factorials).
Cf. A002145 (primes of form 4k+3).
Cf. A129517 (odd primes p such that p divides (p-1)!! - 1).
Cf. A129516 (numbers k such that k divides (k-1)!! - 1).
Cf. A260298.

Select[Range[3,2000],IntegerQ[((#-2)!!-1)/# ]&&IntegerQ[((#-3)!!-1)/# ]&]

cp's OEIS Frontend

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

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