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 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.

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) = 64_(3*16 + 2) = 64_50 = 6*50 + 4 = 304.

(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 (mathar(AT)strw.leidenuniv.nl), Sep 01 2006

Cf. A121864, A121263, A121266, A121264, A121265, A121295, A121296, A111050, A121866, A122030.

Sequence in context: A153483 A030686 A030688 this_sequence A121864 A080860 A044118

Adjacent sequences: A121860 A121861 A121862 this_sequence A121864 A121865 A121866

nonn,base

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

Corrected and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 01 2006