4,1

Let "N_b" denote "N read in base b" and let "N" denote "N written in base 10" (as in normal life). The sequence is given by 16, 32_16, (64_32)_16, ((128_64)_32)_16, etc., or in other words

......16....32.....64....128.......etc.

..............16.....32.....64.........

.......................16.....32.......

................................16.....

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".

The next term is too large to include.

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.

David Applegate, Marc LeBrun and N. J. A. Sloane, Descending Dungeons and Iterated Base-Changing (arXiv:math.NT/0611293).

(64_32)_16 = (6*32 + 4)_16 = 196_16 = 1*256 + 9*16 + 6 = 406.

Cf. A121863, A121263, A121266, A121264, A121265, A121295, A121296, A111050, A121866, A122029, A122030.

Sequence in context: A030686 A030688 A121863 this_sequence A080860 A044118 A044499

Adjacent sequences: A121861 A121862 A121863 this_sequence A121865 A121866 A121867

nonn,base

N. J. A. Sloane (njas(AT)research.att.com), Aug 31 2006, corrected Sep 05 2006