(a+b)
divides the concatenation [a,b]
Hello
SeqFans,
U = 1,2,4,5,10,12,15,18,36,45, ...
->
U is monotonically increasing
->
a(1)=1
->
a(n+1) is the smallest integer > a(n) such that [a(n)+a(n+1)]
divides the concatenation [a(n),a(n+1)]
Example
here:
1+2
divides 12
2+4
divides 24
4+5
divides 45
5+10
divides 510
...
Dropping
the monotonically increasing constraint would give V -- I hope I didn’t make my
usual mistakes too soon:
V = 1,2,4,5,10,8,14,7,26,13,20,16,17,34,32,12,6,3,...
Rule:
«
Smallest integer not yet present in V such that [a(n)+a(n+1)]
divides the concatenation of [a(n),a(n+1)] »
Example
here:
1+2
divides 12 -> 12/3=4
2+4
divides 24 -> 24/6=4
4+5
divides 45 -> 45/9=5
5+10
divides 510 ->
510/15=34
10+8
divides 108 ->
108/18=6
8+14
divides 814 ->
814/22=37
...
Best,
É.
__________
[Maximilian Hasler]:
>strictly
increasing<
U = 1, 2, 4, 5, 10, 12, 15,
18, 36, 45, 54, 108, 114, 219, 438, 561, 660, 672, 840, 1008, 1071, 1656, 1677,
2184, 2260, 2285, 2742, 3924, 4257, 5544, 6677, 13354, 13475, 14938, 18395,
34450, 37365, 49350, 50649,
>yet
unused<
V = 1, 2, 4, 5, 10, 8, 14, 7,
26, 13, 20, 16, 17, 34, 32, 12, 6, 3, 24, 30, 15, 18, 9, 72, 27, 54, 45, 36,
63, 126, 28, 35, 42, 21, 56, 43, 86, 136, 51, 48, 40, 50, 25, 74, 37, 62, 31,
68, 64, 80, 19, 38, 61, 122, 76, 23, 46, 53, 106, 92, 115, 218, 109, 224, 84,
70, 29, 58, 41, 82, 140, 91, 52, 47, 94, 128, 160, 60, 39, 78, 65, 120, 96,
192, 104, 112, 110, 11, 22, 44, 55, 66, 33, 88, 134, 67, 266, 133, 98, 49, 210,
87, 174, 159, 318, 348, 435, 564, 102, 85, 100, 125, 208, 143, 154, 77, 182,
151, 302, 364, 117, 216, 81, 162, 171, 342, 144, 152, 57, 114, 95, 190, 180, 90,
75, 150, 183, 366, 300, 105, 228, 69, 138, 195, 156, 168, 165, 132, 201, 402,
264, 99, 198, 135, 108, 225, 330, 336, 231, 176, 121, 212, 232, 101, 202, 131,
262, 404, 505, 494, 172, 161, 322, 196, 137, 274, 392, 385, 170, 163, 326, 340,
119, 214, 107, 226, 113, 220, 187, 146, 73, 260, 130, 203, 406, 116, 145, 188,
235, 320, 124, 155, 178, 89, 244, 200, 250, 305, 610, 389, 778, 221, 238, 280,
164, 169, 312, 354, 177, 822, 411, 588, 189, 378, 288, 304, 209, 418, 248, 93,
186, 147, 294, 273, 504, 252, 234, 247, 456, 432, 297, 594, 405, 324, 648, 240,
204, 129, 258, 408, 480, 384, 282, 141, 858, 363, 528, 286, 308, 358, 179, 820,
287, 490, 245, 310, 356, 445, 554, 277, 722, 361, 638, 319, 464, 424, 242, 352,
314, 157, 842, 421, 578, 289, 710, 71, 142, 191, 382, 284, 355, 644, 184, 149,
298, 368, 253, 506, 345, 276, 390, 420, 246, 123, 876, 438, 219, 780, 552, 299,
598, 401, 802, 197, 394, 272, 357, 642, 321, 678, 339, 660, 450, ...
__________
Thanks,
Maximilian, I love those two
sequences (I hope you’ll submit them to the OEIS and co-author)!
Best,
É.