A170820 Let p = n-th prime; a(n) = (p-1)/(order of (p+3)/2 mod p).

2, 1, 1, 3, 1, 6, 2, 4, 1, 1, 1, 2, 2, 4, 1, 5, 2, 10, 2, 3, 1, 1, 12, 4, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 1, 5, 2, 2, 4, 3, 42, 1, 1, 1, 1, 2, 8, 1, 1, 2, 4, 1, 1, 7, 2, 4, 6, 2, 2, 4, 30, 2, 1, 1, 1, 2, 1, 3, 2, 2, 2, 1, 25, 4, 11, 1, 10, 2, 3, 1, 1, 8, 10, 33, 1, 2, 3, 1, 6, 2, 4, 1, 2, 1, 2, 2, 1

Offset: 3

Author

N. J. A. Sloane, Dec 24 2009

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 3..65536
• I. Anderson and D. A. Preece, Combinatorially fruitful properties of 3*2^(-1) and 3*2^(-2) modulo p, Discr. Math., 310 (2010), 312-324.

Crossrefs

Cf. A014664, A001917, A170821, A170822.

Programs

Maple

with(numtheory); [seq((ithprime(n)-1)/order((ithprime(n)+3)/2,ithprime(n)),n=3..130)];

Mathematica

a[n_] := Module[{p=Prime[n]}, (p-1)/MultiplicativeOrder[(p+3)/2, p]]; Array[a, 100, 3] (* Amiram Eldar, Dec 03 2018 *)

PARI

a(n) = my(p=prime(n)); (p-1)/znorder(Mod((p+3)/2, p)); \\ Michel Marcus, Dec 03 2018