A296765 Numbers whose base-60 digits d(m), d(m-1), ..., d(0) have #(rises) = #(falls); see Comments.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 122, 183, 244, 305, 366

Offset: 1

Author

Clark Kimberling, Jan 08 2018

Keywords

• nonn
• base
• easy

Comments

A rise is an index i such that d(i) < d(i+1); a fall is an index i such that d(i) > d(i+1). The sequences A296762-A296764 partition the natural numbers. This sequence differs from A262065; see the example. For a guide to related sequences, see A296712.

Examples

			The base-60 digits of 13406581 are 1, 2, 4, 3, 1; here #(rises) = 2 and #(falls) = 2, so 13406581 is in the sequence.  This sequence is not A262065, as not all the terms in this sequence are palindromes.
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A296766, A296767, A296712, A262065.

Programs

Mathematica

z = 200; b = 60; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296765 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296766 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296767 *)