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 bottom upwards.
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
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) = 64_(3*16 + 2) = 64_50 = 6*50 + 4 = 304.
PROG
(PARI) rebase(n, bas)={ local(resul, i) ; resul= n % 10 ; i=1 ; while(n>0, n = n \10 ; resul += (n%10)*bas^i ; i++ ; ) ; return(resul) ; } { a=16 ; print(a) ; for(n=5, 12, a=2^n ; forstep(j=n, 5, -1, a=rebase(2^(j-1), a) ; ) ; print1(a, ", ") ; ) ; } \\ R. J. Mathar, Sep 01 2006
CROSSREFS
KEYWORD
nonn,base
AUTHOR
N. J. A. Sloane, Aug 31 2006, corrected Sep 05 2006
EXTENSIONS
Corrected and extended by R. J. Mathar, Sep 01 2006
STATUS
approved