[seqfan] Re: a(n) divides a(a(n))

[Lars Blomberg]

Hello,

My result is
2, 4, 1, 8, 5, 6, 7, 16, 9, 10, 11, 12, 13, 14, 15, 32, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 64, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 128, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 256, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221

But maybe T[k] = k is not allowed?

With that restriction the result is:
2, 4, 1, 8, 6, 12, 9, 16, 18, 11, 22, 24, 14, 28, 17, 32, 34, 36, 20, 40, 23, 44, 46, 48, 26, 52, 29, 56, 58, 31, 62, 64, 35, 68, 70, 72, 38, 76, 41, 80, 82, 43, 86, 88, 47, 92, 94, 96, 50, 100, 53, 104, 106, 55, 110, 112, 59, 116, 118, 61, 122, 124, 65, 128, 130, 67, 134, 136, 71, 140, 142, 144, 74, 148, 77, 152, 154, 79, 158, 160, 83, 164, 166, 85, 170, 172, 89, 176, 178, 91, 182, 184, 95, 188, 190, 192, 98, 196, 101, 200, 202, 103, 206, 208, 107, 212, 214, 109, 218, 220, 113, 224, 226, 115, 230, 232, 119, 236, 238, 121, 242, 244, 125, 248, 250, 127, 254, 256, 131, 260, 262, 133, 266, 268, 137, 272, 274, 139, 278, 280, 143, 284, 286, 288, 146, 292, 149, 296, 298, 151, 302, 304, 155, 308, 310, 157, 314, 316, 161, 320, 322, 163, 326, 328, 167, 332, 334, 169, 338, 340, 173, 344, 346, 175, 350, 352, 179, 356, 358, 181, 362, 364, 185, 368, 370, 187, 374, 376, 191, 380, 382, 384, 194, 388, 197, 392, 394, 199, 398, 400, 203, 404, 406, 205, 410, 412, 209, 416, 418, 211, 422, 424, 215, 428
Which is in agreement with your data.

It seems that T[k] alternates between 2*k and a value close to k (k+1 or k+2).

Best regards,
Lars

-----Ursprungligt meddelande-----
Från: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] För Eric Angelini
Skickat: den 11 april 2015 18:01
Till: Sequence Discussion list
Ämne: [seqfan] a(n) divides a(a(n))


Hello SeqFans,
T is the lexicographically first seq where:

a(n) divides a(a(n))
a(n) is not equal to a(a(n))

T was always extended with the smallest integer not yet in T and not leading to a contradiction.

T= 2,4,1,8,6,12,9,16,18,11,22,24,14,28,
17,32,34,36,20,40,23,44,46,48,26,52,
29,56,58,31,62,64,35,68,70,72,38,76,
41,80,82,43,86,88,47,92,94,96,...

Example:
2 divides the 2nd term of T (2 d 4)
4 divides the 4th term of T (4 d 8)
1 divides the 1st term of T (1 d 3)
8 divides the 8th term of T (8 d 16)
6 divides the 6th term of T (6 d 12)
12 divides the 12th term of T (12 d 24)
...
Why is 9 the next term?
It cannot be 3 as 3 doesn't divide the 3rd term; it cannot be 5 as 5 doesn't divide the 5th term; it cannot be 7 as 7 would be both a(n) and a(a(n)); it cannot be 8 as 8 is already in T; thus 9 is available as the 7th term of T because 9 doesn't contradict anything.

Best,
É.


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