A296761 - OEIS

A296761

Numbers whose base-16 digits d(m), d(m-1), ..., d(0) have #(rises) < #(falls); see Comments.

16, 32, 33, 48, 49, 50, 64, 65, 66, 67, 80, 81, 82, 83, 84, 96, 97, 98, 99, 100, 101, 112, 113, 114, 115, 116, 117, 118, 128, 129, 130, 131, 132, 133, 134, 135, 144, 145, 146, 147, 148, 149, 150, 151, 152, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169

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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 A296759-A296761 partition the natural numbers. See the guide at A296712.

LINKS

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

EXAMPLE

The base-16 digits of 32 are 2,0; here #(rises) = 0 and #(falls) = 2, so 32 is in the sequence.

MATHEMATICA

z = 200; b = 16; d[n_] := Sign[Differences[IntegerDigits[n, b]]];

Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296759 *)

Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &] (* A296760 *)

Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &] (* A296761 *)

CROSSREFS

Cf. A296759, A296760, A296712.

Sequence in context: A240053 A059164 A040240 * A297288 A335246 A055075

Adjacent sequences: A296758 A296759 A296760 * A296762 A296763 A296764

KEYWORD

nonn,base,easy

AUTHOR

Clark Kimberling, Jan 08 2018

STATUS

approved