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

1,2

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.

Links

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

Example

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.

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 *)

Crossrefs

Cf. A296766, A296767, A296712, A262065.

Sequence in context: A085736 A265711 A262065 * A055643 A122079 A272118

Adjacent sequences: A296762 A296763 A296764 * A296766 A296767 A296768

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 08 2018

Status

approved