[seqfan] Error in A047699
Andrew Weimholt
andrew.weimholt at gmail.com
Wed Jul 14 02:23:15 CEST 2010
Looks like there is an error in A047699 (A sparse maximal expulsion
set under addition)
The definition (w/ my paraphrasing) is
a(n+1) = a(n) + x, where x is the smallest value which is
not already in the sequence and which is not equal to
a(i) +/- a(k), for some i<=n, k<=n.
the current entry begins
1, 4, 10, 17, 29, 44, 67, 91, 117, 148, 180,...
but after 1, 4, 10, 17, 29, 44,
the smallest value not in the sequence which is not
the sum or difference of two terms in {1,4,10,17,29,44}
is 22, not 23,
so the next term should be 66, not 67.
All subsequent terms are affected.
Here is what I get when computing the sequence...
1, 4, 10, 17, 29, 44, 66, 89, 113, 139, 170, 202, 237, 273, 311, 352,
394, 445, 497, 550, 605, 664, 728, 796, 871, 948, 1026, 1106, 1188,
1274, 1361, 1452,
1544, 1638, 1735, 1835, 1936, 2038, 2145, 2256, 2372, 2491, 2611,
2736, 2863, 2991, 3122, 3259,
3403, 3549, 3696, 3847, 4001, 4160, 4321, 4484, 4648, 4813, 4988,
5164, 5341, 5522, 5710, 5899,
6089, 6283, 6478, 6674, 6874, 7078, 7288, 7503, 7719, 7936, 8157,
8380, 8605, 8837, 9071, 9313,
(more terms if needed)
I tried to email the author, but my email was bounced back.
Andrew
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