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A121265
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Descending dungeons: a(10)=10; for n>10, a(n) = a(n-1) read as if it were written in base n.
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14
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10, 11, 13, 16, 20, 30, 48, 76, 132, 420, 1640, 11991, 249459, 14103793, 5358891675, 19563802363305, 3359230167951561129, 181335944930584275675841374, 54416647690014492928933662292768871352, 6605721238793689879501639879905020611382966457124120828, 360539645288616164606228883801608423987740093330992456820074646988075733781927268
(list; graph; refs; listen; history; internal format)
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OFFSET
| 10,1
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COMMENTS
| Using N_b to denote "N read in base b", the sequence is given by
......10....10.....10.....10.......etc.
..............11.....11.....11.........
.......................12.....12.......
................................13.....
where the subscripts are evaluated from the top downwards.
More precisely, "N_b" means "Take decimal expansion of N and evaluate it as if it were a base-b expansion".
A "dungeon" of numbers.
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REFERENCES
| David Applegate, Marc LeBrun and N. J. A. Sloane, Descending Dungeons, Problem 11286, Amer. Math. Monthly, 116 (2009) 466-467.
David Applegate, Marc LeBrun and N. J. A. Sloane, Descending Dungeons and Iterated Base-Changing, in "The Mathematics of Preference, Choice and Order: Essays in Honor of Peter Fishburn", edited by Steven Brams, William V. Gehrlein and Fred S. Roberts, Springer, 2009, pp. 393-402.
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LINKS
| N. J. A. Sloane, Table of n, a(n) for n = 10..35
David Applegate, Marc LeBrun and N. J. A. Sloane, Descending Dungeons and Iterated Base-Changing (arXiv:math.NT/0611293).
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FORMULA
| If a, b >= 10, then a_b is roughly 10^(log(a)log(b)) (all logs are base 10 and "roughly" means it is an upper bound and using floor(log()) gives a lower bound). Equivalently, there exists c > 0 such that for all a, b >= 10, 10^(c log(a)log(b)) <= a_b <= 10^(log(a)log(b)). Thus a_n is roughly 10^product(log(9+i),i=1..n), or equivalently, a_n = 10^10^(n loglog n + O(n)). - David Applegate (david(AT)research.att.com) and N. J. A. Sloane (njas(AT)research.att.com), Aug 25 2006
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MAPLE
| M:=35; a:=list(10..M): a[10]:=10: lprint(10, a[10]); for n from 11 to M do t1:=convert(a[n-1], base, 10); a[n]:=add(t1[i]*n^(i-1), i=1..nops(t1)); lprint(n, a[n]); od:
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CROSSREFS
| Cf. A121263, A121295, A121296, A127744, A122734.
Sequence in context: A121263 A121295 A121296 * A045986 A188165 A125588
Adjacent sequences: A121262 A121263 A121264 * A121266 A121267 A121268
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KEYWORD
| nonn,base,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Aug 23 2006
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