

A121863


See Comments lines for definition.


5




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 baseb 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 BaseChanging, 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. 393402.


LINKS

Table of n, a(n) for n=4..10.
David Applegate, Marc LeBrun and N. J. A. Sloane, Descending Dungeons and Iterated BaseChanging, arXiv:math/0611293 [math.NT], 20062007.
David Applegate, Marc LeBrun, N. J. A. Sloane, Descending Dungeons, Problem 11286, Amer. Math. Monthly, 116 (2009) 466467.


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^(j1), a) ; ) ; print1(a, ", ") ; ) ; } \\ R. J. Mathar, Sep 01 2006


CROSSREFS

Cf. A121864, A121263, A121266, A121264, A121265, A121295, A121296, A111050, A121866, A122030.
Sequence in context: A186842 A231840 A199809 * A121864 A221485 A204723
Adjacent sequences: A121860 A121861 A121862 * A121864 A121865 A121866


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



