A122029 See Comments lines for definition.

16, 38, 200, 32768, 12918916616, 1242818253229988572210659846, 1900850177472859316749829932381453683166126327573485314289555274100802310696341510

Offset: 4

Author

N. J. A. Sloane, Aug 31 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, 16_32, (16_32)_64, ((16_32)_64)_128, etc., or in other words

......16....16.....16.....16.......etc.

..............32.....32.....32.........

.......................64.....64.......

................................128....

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

• 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. A121863, A121263, A121266, A121264, A121265, A121295, A121296, A111050, A121866, A121864.

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 ; for(p=5,10, print(a) ; a=rebase(a,2^p) ; ) ; } \\ R. J. Mathar, Sep 01 2006

Extensions

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