A number which appears in a Fibonacci-like sequence seeded by some signed sums of its digits. more
The Gilda numbers up to 1.61×10
10 :
29,
49,
78,
110,
152,
220,
314,
330,
364,
440,
550,
628,
660,
683,
770,
880,
990,
997,
2207,
5346,
13064,
30254,
35422,
37862,
38006,
65676,
73805,
143662,
202196,
933138,
977909,
3120796,
3242189,
3363582,
3606368,
3727761,
3849154,
3970547,
4484776,
4848955,
14005576,
18633637,
30571351,
34610158,
92078232,
271953103,
786119998,
1377313380,
3142498101,
6360994231,
9142471346,
9410385642,
9789861558,
9946214234,
16141628324.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 55 values, from 29 to 16141628324).
n\r | 0 | 1 |
2 | 39 | 16 | 2 |
3 | 14 | 20 | 21 | 3 |
4 | 17 | 9 | 22 | 7 | 4 |
5 | 12 | 12 | 11 | 9 | 11 | 5 |
6 | 12 | 7 | 14 | 2 | 13 | 7 | 6 |
7 | 7 | 11 | 11 | 7 | 5 | 7 | 7 | 7 |
8 | 8 | 2 | 9 | 3 | 9 | 7 | 13 | 4 | 8 |
9 | 4 | 5 | 6 | 4 | 7 | 7 | 6 | 8 | 8 | 9 |
10 | 10 | 4 | 7 | 2 | 7 | 2 | 8 | 4 | 7 | 4 | 10 |
11 | 14 | 7 | 4 | 1 | 6 | 3 | 4 | 5 | 5 | 5 | 1 |
A pictorial representation of the table above
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.