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Lucas numbers

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A member of the sequence defined by the recurrence L(0)=2, L(1)=1 and L(n) = L(n-1) + L(n-2). more

The Lucas numbers up to 1015 :
1, 2, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364, 2207, 3571, 5778, 9349, 15127, 24476, 39603, 64079, 103682, 167761, 271443, 439204, 710647, 1149851, 1860498, 3010349, 4870847, 7881196, 12752043, 20633239, 33385282, 54018521, 87403803, 141422324, 228826127, 370248451, 599074578, 969323029, 1568397607, 2537720636, 4106118243, 6643838879, 10749957122, 17393796001, 28143753123, 45537549124, 73681302247, 119218851371, 192900153618, 312119004989, 505019158607, 817138163596, 1322157322203, 2139295485799, 3461452808002, 5600748293801, 9062201101803, 14662949395604, 23725150497407, 38388099893011, 62113250390418, 100501350283429, 162614600673847, 263115950957276, 425730551631123, 688846502588399.

Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 100000 values, from 1 to 5.8⋅1020898).

n\r 0  1 
23333366667 2 
3250003750037500 3 
416667166671666650000 4 
5025000250002500025000 5 
683332499912499166671250125001 6 
7125001250062502500025000625012500 7 
8083341666625000166678333025000 8 
983338334208348333833483338334208328333 9 
1001666783331666783340833316667833316666 10 
11100001000010000200001000000300000010000

A pictorial representation of the table above
motab
Imagine to divide the members of this family by a number n and compute the remainders. Should they be uniformly distributed, each remainder from 0 to n-1 would be obtained in about (1/n)-th of the cases. This outcome is represented by a white square. Reddish (resp. bluish) squares represent remainders which appear more (resp. less) frequently than 1/n.