A157023 S(n) - the sum of the areas of the polygons constructed from connecting with a straight line all identical members in the multiplicative table modulo n (finite field).

0, 0, 2, 14, 28, 70, 108, 205, 334, 484, 616, 892, 1138, 1511, 1882, 2418, 2908, 3556, 3962, 4937, 5876, 6926, 7180, 9377, 10478, 12019, 13556, 15244, 16494, 19248, 20614, 23785, 26056, 28865, 30828, 34648, 37142, 41095, 43872, 48530, 50596

Offset

2,3

Comments

1/S(4) + 1/S(5) + ... + 1/S(inf) ~ e^(1/2) - 1

Links

Table of n, a(n) for n=2..42.

Ofer Barasofsky, On the geometry of natural numbers

Formula

S(n) = S(0,n) + S(1,n) + ... + S(n-1,n) where S(i,n) is the area of the polygon constructed from connecting with a straight line all the members with value i.

Example

Example: n=4 1 2 3 2 0 2 3 2 1 S(0,4) = 0 S(1,4) = 0 S(2,4) = 2 S(3,4) = 0 S(4) = 0 + 0 + 2 + 0 = 2.

Crossrefs

Sequence in context: A200039 A281206 A189331 * A101554 A057018 A038341

Adjacent sequences: A157020 A157021 A157022 * A157024 A157025 A157026

Keyword

nonn

Author

Ofer Barasofsky (oferbarasofsky(AT)gmail.com), Feb 21 2009

Status

approved