A296758 - OEIS

A296758

Numbers whose base-15 digits d(m), d(m-1), ..., d(0) have #(rises) < #(falls); see Comments.

15, 30, 31, 45, 46, 47, 60, 61, 62, 63, 75, 76, 77, 78, 79, 90, 91, 92, 93, 94, 95, 105, 106, 107, 108, 109, 110, 111, 120, 121, 122, 123, 124, 125, 126, 127, 135, 136, 137, 138, 139, 140, 141, 142, 143, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 165

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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 A296756-A296758 partition the natural numbers. See the guide at A296712.

LINKS

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

EXAMPLE

The base-15 digits of 15^5 are 1, 0, 0, 0, 0, 0; here #(rises) = 0 and #(falls) = 1, so 15^5 is in the sequence.

MATHEMATICA

z = 200; b = 15; d[n_] := Sign[Differences[IntegerDigits[n, b]]];

Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296756 *)

Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &] (* A296757 *)

Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &] (* A296758 *)

CROSSREFS

Cf. A296756, A296757, A296712.

Sequence in context: A200896 A322370 A040210 * A297285 A115776 A095783

Adjacent sequences: A296755 A296756 A296757 * A296759 A296760 A296761

KEYWORD

nonn,base,easy

AUTHOR

Clark Kimberling, Jan 08 2018

STATUS

approved