A121266 - OEIS

%I #12 Jul 06 2018 04:46:49

%S 10,11,11,12,13,13,13,15,16,16,14,17,19,20,20,15,19,22,24,25,25,16,21,

%T 25,28,30,31,31,17,23,28,32,35,37,38,38,18,25,31,36,40,43,45,46,46,19,

%U 27,34,40,45,49,52,54,55,55,20,29,37,44,50,55,59,62,64,65,65

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

%C Left-hand entry of row n is n, right-hand entry is A121263(n).

%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 N. J. A. Sloane, <a href="/A121266/b121266.txt">Rows 10 through 45 of triangle, flattened</a>

%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 Triangle begins:

%e 10

%e 11 11

%e 12 13 13

%e 13 15 16 16

%e 14 17 19 20 20

%e 15 19 22 24 25 25

%e 16 21 25 28 30 31 31

%e 17 23 28 32 35 37 38 38

%e 18 25 31 36 40 43 45 46 46

%e 19 27 34 40 45 49 52 54 55 55

%e 20 29 37 44 50 55 59 62 64 65 65

%p 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 Cf. A121263.

%K nonn,tabl,base,look

%O 10,1

%A _N. J. A. Sloane_, Aug 23 2006