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A296712 Numbers n whose base-10 digits d(m), d(m-1), ..., d(0) have #(rises) = #(falls); see Comments. 116
1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 102, 103, 104, 105, 106, 107, 108, 109, 111, 120, 121, 130, 131, 132, 140, 141, 142, 143, 150, 151, 152, 153, 154, 160, 161, 162, 163, 164, 165, 170, 171, 172, 173, 174, 175, 176, 180, 181 (list; graph; refs; listen; history; text; internal format)
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 A296712-A296714 partition the natural numbers.

****

Guide to related sequences:

Base   #(rises) = #(falls)   #(rises) > #(falls)   #(rises) < #(falls)

2            A005408             (none)                A005843

3            A296691             A296692               A296693

4            A296694             A296695               A296696

5            A296697             A296698               A296699

6            A296700             A296701               A296702

7            A296703             A296704               A296705

8            A296706             A296707               A296708

9            A296709             A296710               A296711

10           A296712             A296713               A296714

11           A296744             A296745               A296746

12           A296747             A296748               A296749

13           A296750             A296751               A296752

14           A296753             A296754               A296755

15           A296756             A296757               A296758

16           A296759             A296760               A296761

20           A296762             A296763               A296764

60           A296765             A296766               A296767

LINKS

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

EXAMPLE

The base-10 digits of 181 are 1,8,1; here #(rises) = 1 and #(falls) = 1, so that 181 is in the sequence.

MATHEMATICA

z = 200; b = 10; d[n_] := Sign[Differences[IntegerDigits[n, b]]];

Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296712 *)

Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296713 *)

Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296714 *)

CROSSREFS

Cf. A296713, A296714, A296712.

Sequence in context: A297148 A048307 A043713 * A276115 A266140 A297271

Adjacent sequences:  A296709 A296710 A296711 * A296713 A296714 A296715

KEYWORD

nonn,base,easy

AUTHOR

Clark Kimberling, Jan 08 2018

STATUS

approved

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Last modified November 18 02:07 EST 2019. Contains 329242 sequences. (Running on oeis4.)