cp's OEIS Frontend

A122029 See Comments lines for definition.

%I A122029 #13 Mar 31 2025 23:10:40
%S A122029 16,38,200,32768,12918916616,1242818253229988572210659846,
%T A122029 1900850177472859316749829932381453683166126327573485314289555274100802310696341510
%N A122029 See Comments lines for definition.
%C A122029 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
%C A122029 ......16....16.....16.....16.......etc.
%C A122029 ..............32.....32.....32.........
%C A122029 .......................64.....64.......
%C A122029 ................................128....
%C A122029 where the subscripts are evaluated from the top downwards
%C A122029 More precisely, "N_b" means "Take decimal expansion of N and evaluate it as if it were a base-b expansion".
%C A122029 The next term is too large to include.
%C A122029 A "dungeon" of numbers.
%D A122029 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 A122029 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 A122029 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.
%o A122029 (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
%Y A122029 Cf. A121863, A121263, A121266, A121264, A121265, A121295, A121296, A111050, A121866, A121864.
%K A122029 nonn,base
%O A122029 4,1
%A A122029 _N. J. A. Sloane_, Aug 31 2006
%E A122029 Corrected and extended by _R. J. Mathar_, Sep 01 2006