A121864 See Comments lines for definition.

16, 50, 406, 1258008, 25465014649108, 208080288305986199465852412572946560

Offset

4,1

Comments

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.

References

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.

Links

Table of n, a(n) for n=4..9.

David Applegate, Marc LeBrun and N. J. A. Sloane, Descending Dungeons and Iterated Base-Changing, arXiv:math/0611293 [math.NT], 2006-2007.

David Applegate, Marc LeBrun, N. J. A. Sloane, Descending Dungeons, Problem 11286, Amer. Math. Monthly, 116 (2009) 466-467.

Example

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

Crossrefs

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

Sequence in context: A231840 A199809 A121863 * A221485 A204723 A204962

Adjacent sequences: A121861 A121862 A121863 * A121865 A121866 A121867

Keyword

nonn,base

Author

N. J. A. Sloane, Aug 31 2006, corrected Sep 05 2006

Status

approved