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%I #10 Jul 06 2018 04:46:36
%S 16,50,304,93032,17310371214,1498244757849709540196,
%T 3363165974015385428987990761994364730059919325224645845292529932
%N See Comments lines for definition.
%C 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
%C ......16....32.....64....128.......etc.
%C ..............16.....32.....64.........
%C .......................16.....32.......
%C ................................16.....
%C where the subscripts are evaluated from the bottom upwards.
%C More precisely, "N_b" means "Take decimal expansion of N and evaluate it as if it were a base-b expansion".
%C The next term is too large to include.
%C A "dungeon" of numbers.
%D 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.
%H David Applegate, Marc LeBrun and N. J. A. Sloane, <a href="https://arxiv.org/abs/math/0611293">Descending Dungeons and Iterated Base-Changing</a>, arXiv:math/0611293 [math.NT], 2006-2007.
%H David Applegate, Marc LeBrun, N. J. A. Sloane, <a href="https://www.jstor.org/stable/40391135">Descending Dungeons, Problem 11286</a>, Amer. Math. Monthly, 116 (2009) 466-467.
%e 64_(32_16) = 64_(3*16 + 2) = 64_50 = 6*50 + 4 = 304.
%o (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
%Y Cf. A121864, A121263, A121266, A121264, A121265, A121295, A121296, A111050, A121866, A122030.
%K nonn,base
%O 4,1
%A _N. J. A. Sloane_, Aug 31 2006, corrected Sep 05 2006
%E Corrected and extended by _R. J. Mathar_, Sep 01 2006
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