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

[Maximilian Hasler]

I confirm Doug's terms:
by setting my search limit to 3000, I get the same first 100 terms
(How come I did not think of trying this ??),
and they remain stable when I calculate 200 of them.

But the fact that my terms were consistent to over 85 terms but wrong
from the 33rd one on, makes it clear how little we can trust in these
results...
(which does not mean that the question of existence of the sequence is
hopeless to answer, IMO).

Maximilian

? try2complete(100,,2001)
time = 3,773 ms.
%46 = [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]

try2complete(200,,2001) =
[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, 248, 253, 401, 252, 254, 265, 402, 266,
269, 271, 278, 403, 281, 285, 340, 291, 292, 294, 295, 301, 309, 312,
317, 360, 318, 321, 328, 329, 333, 337, 341, 901, 346, 801, 347, 350,
355, 369, 357, 365, 373, 410, 378, 379, 603, 380, 382, 383, 384, 393,
404, 502, 604, 409, 501, 413, 418, 802, 419, 424, 428, 433, 605, 434,
437, 438, 441, 442, 447, 457, 503, 458, 464, 469, 1000, 470, 471, 472,
485, 902, 486, 488, 493, 499, 606, 607, 504, 510, 511, 513, 515, 521,
526, 531, 690, 532, 538, 542, 700, 543]

? vecextract(%,"1..100")==%46
%48 = 1

---

> 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
>
>
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