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A121266 Triangle read by rows: row n (n>= 10) gives n-10 successive bases used in computing A121263(n) followed by A121263(n) itself.

%I A121266 #12 Jul 06 2018 04:46:49
%S A121266 10,11,11,12,13,13,13,15,16,16,14,17,19,20,20,15,19,22,24,25,25,16,21,
%T A121266 25,28,30,31,31,17,23,28,32,35,37,38,38,18,25,31,36,40,43,45,46,46,19,
%U A121266 27,34,40,45,49,52,54,55,55,20,29,37,44,50,55,59,62,64,65,65
%N A121266 Triangle read by rows: row n (n>= 10) gives n-10 successive bases used in computing A121263(n) followed by A121263(n) itself.
%C A121266 Left-hand entry of row n is n, right-hand entry is A121263(n).
%C A121266 A "dungeon" of numbers.
%D A121266 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 A121266 N. J. A. Sloane, <a href="/A121266/b121266.txt">Rows 10 through 45 of triangle, flattened</a>
%H A121266 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 A121266 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 A121266 Triangle begins:
%e A121266 10
%e A121266 11 11
%e A121266 12 13 13
%e A121266 13 15 16 16
%e A121266 14 17 19 20 20
%e A121266 15 19 22 24 25 25
%e A121266 16 21 25 28 30 31 31
%e A121266 17 23 28 32 35 37 38 38
%e A121266 18 25 31 36 40 43 45 46 46
%e A121266 19 27 34 40 45 49 52 54 55 55
%e A121266 20 29 37 44 50 55 59 62 64 65 65
%p A121266 M:=45; a:=list(10..M): a[10]:=10: a[10]; for n from 11 to M do b:=n; lprint(b); for i from n-1 by -1 to 11 do t1:=convert(i,base,10); b:=add(t1[j]*b^(j-1),j=1..nops(t1)): lprint(b); od: a[n]:=b; lprint(a[n]); od:
%Y A121266 Cf. A121263.
%K A121266 nonn,tabl,base,look
%O A121266 10,1
%A A121266 _N. J. A. Sloane_, Aug 23 2006