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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

%I #4 Apr 15 2013 02:13:18

%S 0,0,2,14,28,70,108,205,334,484,616,892,1138,1511,1882,2418,2908,3556,

%T 3962,4937,5876,6926,7180,9377,10478,12019,13556,15244,16494,19248,

%U 20614,23785,26056,28865,30828,34648,37142,41095,43872,48530,50596

%N 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).

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

%H Ofer Barasofsky, <a href="http://tesseract.athost.net/maamar2web.htm">On the geometry of natural numbers</a>

%F 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.

%e 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.

%K nonn

%O 2,3

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

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