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A319480 Number of ordered pairs (i,j) with 0 < i < j < prime(n)/2 such that R(i^2,prime(n)) > R(j^2,prime(n)), where R(k,p) (with p an odd prime and k an integer) denotes the unique integer r among 0,1,...,(p-1)/2 for which k is congruent to r or -r modulo p. 5
0, 0, 1, 3, 7, 10, 14, 19, 41, 42, 74, 79, 85, 100, 154, 163, 207, 224, 245, 309, 318, 342, 449, 536, 590, 553, 581, 715, 738, 856, 912, 1085, 1037, 1324, 1229, 1477, 1442, 1491, 1785, 1730, 1952, 1986, 2240, 2316, 2191, 2474, 2748, 2836, 3176 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,4

COMMENTS

Conjecture: Let p be any odd prime and let N(p) be the number of ordered pairs (i,j) with 0 < i < j < p/2 and R(i^2,p) > R(j^2,p). Then N(p) == floor((p+1)/8) (mod 2).

See also A319311 for a similar conjecture.

LINKS

Zhi-Wei Sun, Table of n, a(n) for n = 2..1000

EXAMPLE

a(3) = 0 since prime(3) = 5 and R(1^2,5) = 1 = R(2^2,5).

a(4) = 1 since prime(4) = 7, R(1^2,7) = 1 < R(2^2,7) = 3, R(1^2,7) < R(3^2,7) = 2, and R(2^2,7) = 3 > R(3^2,7) = 2.

MATHEMATICA

R[k_, p_]:=R[k, p]=Abs[Mod[k, p, -p/2]];

t[p_]:=t[p]=Sum[Boole[R[i^2, p]>R[j^2, p]], {j, 2, (p-1)/2}, {i, 1, j-1}]; Table[t[Prime[n]], {n, 2, 50}]

CROSSREFS

Cf. A000040, A000290, A319311.

Sequence in context: A140487 A310189 A293788 * A310190 A307203 A347638

Adjacent sequences:  A319477 A319478 A319479 * A319481 A319482 A319483

KEYWORD

nonn

AUTHOR

Zhi-Wei Sun, Sep 20 2018

STATUS

approved

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Last modified September 19 03:31 EDT 2021. Contains 347550 sequences. (Running on oeis4.)