A296762 Numbers whose base-20 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, 21, 42, 63, 84, 105, 126, 147, 168, 189, 210, 231, 252, 273, 294, 315, 336, 357, 378, 399, 401, 402, 403, 404, 405, 406, 407, 408, 409, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 421

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. See the guide at A296712.

Links

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

Example

The base-20 digits of 421 are 1,1,1; here #(rises) = 0 and #(falls) = 0, so 421 is in the sequence.

Mathematica

z = 200; b = 20; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296762 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296763 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296764 *)

Crossrefs

Cf. A296763, A296764, A296712.

Sequence in context: A246097 A275776 A022465 * A247751 A059962 A057605

Adjacent sequences: A296759 A296760 A296761 * A296763 A296764 A296765

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 08 2018

Status

approved