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

%I #13 Jun 08 2021 02:24:20

%S 3,7,47,59,79,83,103,107,127,139,191,199,211,251,263,283,307,331,367,

%T 379,383,431,467,479,499,503,547,587,599,607,631,643,659,727,743,811,

%U 823,827,839,859,863,883,887,907,971,991,1087,1151,1163,1171,1259,1283

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

%C 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).

%C Odd numbers k > 1 such that k divides (k-1)!! + 1. - _Thomas Ordowski_, Jul 26 2016

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

%Y Cf. A006882 (double factorials).

%Y Cf. A002145 (primes of form 4k+3).

%Y Cf. A129517 (odd primes p such that p divides (p-1)!! - 1).

%Y Cf. A129516 (numbers k such that k divides (k-1)!! - 1).

%Y Cf. A260298.

%K nonn

%O 1,1

%A _Alexander Adamchuk_, Apr 18 2007