10,1

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.

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.

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).

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

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:

Cf. A121263, A121295, A121296, A127744, A122734.

Sequence in context: A121263 A121295 A121296 this_sequence A045986 A125588 A095038

Adjacent sequences: A121262 A121263 A121264 this_sequence A121266 A121267 A121268

nonn,base,nice

N. J. A. Sloane (njas(AT)research.att.com), Aug 23 2006