[seqfan] Re: Sum of the a(n) first digits of S is a prime -- an illusion?

[Douglas McNeil]

E. Angelini wrote:

>> I get by hand:
>>
>> S = 2,1,4,6,3,7,8,60,9,11,14,17,61,16,22,25,30,26,28,34,49,37,200,36,38,39,42,59,51,54,56,61,69,201,...

but this has 61 twice.

M. Hasler wrote:

> [2, 1, 4, 6, 3, 7, 8, 60, 9, 11, 14, 17, 61, 16, 22, 25, 30, 26, 28,
> 34, 49, 37, 200, 36, 38, 39, 42, 59, 51, 54, 56, 62, 71, 600, 65, 70,
> 66, 75, 201, 72, 67, 68, 82, 100, 83, 84, 91, 93, 300, 94, 95, 301,
> 98, 101, 103, 110, 116, 120, 302, 121, 130, 132, 202, 133, 141, 500,
> 142, 143, 148, 150, 154, 155, 165, 303, 166, 174, 203, 175, 183, 204,
> 184, 192, 196, 290, 208, 800, ...]

which seems to self-describe so far, but I find

sage: S[:100]
[2, 1, 4, 6, 3, 7, 8, 60, 9, 11, 14, 17, 61, 16, 22, 25, 30, 26, 28,
34, 49, 37, 200, 36, 38, 39, 42, 59, 51, 54, 56, 62, 68, 2000, 63, 67,
80, 69, 70, 72, 73, 82, 90, 600, 81, 83, 91, 601, 84, 92, 97, 103,
201, 104, 106, 107, 112, 113, 120, 126, 130, 202, 131, 139, 400, 138,
140, 141, 144, 148, 153, 163, 203, 164, 168, 172, 178, 181, 900, 182,
183, 187, 196, 500, 280, 800, 197, 198, 204, 206, 208, 224, 290, 225,
232, 602, 233, 234, 238, 246]

which I think also self-describes but disagrees from the 33rd term,
which I take as 68.  I didn't use a search limit, which probably
explains the difference as the next term seems to be 2000.

But who knows?  If the above is right (even setting aside the
possibility of backward-propagating blockers later, which I'm too
sleepy to think about) it'd be the only time I'd ever successfully
computed one of Eric's self-referencing sequences in any of the first
half-dozen attempts..


Doug

-- 
Department of Earth Sciences
University of Hong Kong