A319903 -id:A319903 - cp's OEIS frontend

A309012 Number of ordered pairs (i,j) with 0 < i < j < prime(n)/2 such that (i^16 mod prime(n)) > (j^16 mod prime(n)).

0, 0, 0, 0, 3, 3, 0, 16, 21, 43, 30, 62, 77, 99, 129, 146, 203, 187, 228, 245, 252, 345, 372, 382, 402, 558, 570, 631, 663, 756, 901, 1114, 961, 1325, 1398, 1253, 1571, 1470, 1601, 1795, 2024, 1988, 2349, 2014, 2184, 2200, 2728, 3054, 3084, 3718, 3386, 3224, 3018, 3861, 3866, 4258, 4361, 4418, 5110, 4724

Offset: 1

Zhi-Wei Sun, Jul 06 2019

nonn

Conjecture : Let p be an odd prime, and let N be the number of ordered pairs (i,j) with 0 < i < j < p/2 and (i^16 mod p) > (j^16 mod p). When p == 1 (mod 16), we have 2 | N. Also, N == |{0

			a(5) = 3 with prime(5) = 11, and (2^16 mod 11) = 9 greater than (3^16 mod 11) = 3, (4^16 mod 11) = 4 and (5^16 mod 11) = 5.

Zhi-Wei Sun, Table of n, a(n) for n = 1..1000
Zhi-Wei Sun, Quadratic residues and related permutations and identities, arXiv:1809.07766 [math.NT], 2018-2019.

Cf. A000040, A010804, A319311, A319882, A319894, A319903, A320044.

r[p_]:=r[p]=Sum[Boole[PowerMod[j,16,p]>PowerMod[k,16,p]],{k,2,p/2},{j,1,k-1}];
Print[Table[r[Prime[n]],{n,1,60}]]

Showing 1-1 of 1 results.

cp's OEIS Frontend

A309012 Number of ordered pairs (i,j) with 0 < i < j < prime(n)/2 such that (i^16 mod prime(n)) > (j^16 mod prime(n)).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica