A170821 -id:A170821 - cp's OEIS frontend

A170822 Let p = n-th prime; a(n) = (p-1)/(order of A170821(n) mod p).

1, 3, 2, 2, 1, 1, 2, 1, 1, 12, 1, 1, 2, 1, 2, 4, 1, 14, 2, 1, 2, 1, 2, 1, 1, 2, 2, 1, 1, 10, 1, 3, 1, 1, 4, 9, 2, 1, 2, 18, 2, 16, 1, 1, 1, 1, 2, 2, 1, 2, 6, 2, 1, 2, 1, 1, 2, 1, 1, 1, 3, 10, 12, 1, 1, 42, 2, 12, 1, 2, 1, 4, 27, 2, 1, 4, 1, 6, 2, 6, 10, 4, 3, 2, 1, 2, 1, 1, 2, 2, 1, 2, 3, 2, 1, 5

Offset: 3

N. J. A. Sloane, Dec 24 2009

nonn

			n=3: p=5, A170821(n)=2, order of 2 mod 5 = 4, (5-1)/4 = 1 = a(3).

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.

Cf. A001917, A170820, A170821.

f(n) = my(p=prime(n), k=0); while(Mod(4*k, p) != 3, k++); k; \\ A170821
a(n) = my(p=prime(n)); (p-1)/znorder(Mod(f(n), p)); \\ Michel Marcus, Dec 04 2018

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

Original entry on oeis.org

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

N. J. A. Sloane, Dec 24 2009

nonn

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.

Cf. A014664, A001917, A170821, A170822.

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

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

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

cp's OEIS Frontend

A170822 Let p = n-th prime; a(n) = (p-1)/(order of A170821(n) mod p).

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