A121863 See Comments lines for definition.

16, 50, 304, 93032, 17310371214, 1498244757849709540196, 3363165974015385428987990761994364730059919325224645845292529932

Offset: 4

Author

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

Keywords

• nonn
• base

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.

Examples

			64_(32_16) = 64_(3*16 + 2) = 64_50 = 6*50 + 4 = 304.
		

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.

Crossrefs

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

Programs

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

Extensions

Corrected and extended by R. J. Mathar, Sep 01 2006