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A122029 See Comments lines for definition. 1
16, 38, 200, 32768, 12918916616, 1242818253229988572210659846, 1900850177472859316749829932381453683166126327573485314289555274100802310696341510 (list; graph; refs; listen; history; text; internal format)



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





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.


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.


Table of n, a(n) for n=4..10.

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.


(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


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

Sequence in context: A304014 A230828 A122030 * A218900 A070585 A253435

Adjacent sequences:  A122026 A122027 A122028 * A122030 A122031 A122032




N. J. A. Sloane, Aug 31 2006


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



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Last modified September 27 07:28 EDT 2021. Contains 347673 sequences. (Running on oeis4.)