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

10, 11, 11, 12, 13, 13, 13, 15, 16, 16, 14, 17, 19, 20, 20, 15, 19, 22, 24, 25, 25, 16, 21, 25, 28, 30, 31, 31, 17, 23, 28, 32, 35, 37, 38, 38, 18, 25, 31, 36, 40, 43, 45, 46, 46, 19, 27, 34, 40, 45, 49, 52, 54, 55, 55, 20, 29, 37, 44, 50, 55, 59, 62, 64, 65, 65

Offset: 10

Author

N. J. A. Sloane, Aug 23 2006

Keywords

• nonn
• tabl
• base
• look

Comments

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

A "dungeon" of numbers.

Examples

			Triangle begins:
10
11 11
12 13 13
13 15 16 16
14 17 19 20 20
15 19 22 24 25 25
16 21 25 28 30 31 31
17 23 28 32 35 37 38 38
18 25 31 36 40 43 45 46 46
19 27 34 40 45 49 52 54 55 55
20 29 37 44 50 55 59 62 64 65 65
		

References

• 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.

Links

• N. J. A. Sloane, Rows 10 through 45 of triangle, flattened
• 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.

Crossrefs

Cf. A121263.

Programs

Maple

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: