A296882 Numbers whose base-10 digits d(m), d(m-1), ..., d(0) have #(pits) = #(peaks); 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, 60, 61, 62, 63, 64, 65, 66, 67

Offset: 1

Author

Clark Kimberling, Jan 10 2018

Keywords

• nonn
• base
• easy

Comments

A pit is an index i such that d(i-1) > d(i) < d(i+1); a peak is an index i such that d(i-1) < d(i) > d(i+1). The sequences A296882-A296883 partition the natural numbers. See the guides at A296712. We have a(n) = A000027(n) for n=1..100 but not n=101.

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Guide to related sequences:

Base #(pits) = #(peaks) #(pits) > #(peaks) #(pits) < #(peaks)

2 A296858 A296859 A296860

3 A296861 A296862 A296863

4 A296864 A296865 A296866

5 A296867 A296868 A296869

6 A296870 A296871 A296872

7 A296873 A296874 A296875

8 A296876 A296877 A296878

9 A296879 A296880 A296881

10 A296882 A296883 A296884

11 A296885 A296886 A296887

12 A296888 A296889 A296890

13 A296891 A296892 A296893

14 A296894 A296895 A296896

15 A296897 A296898 A296899

16 A296900 A296901 A296902

20 A296903 A296904 A296905

60 A296906 A296907 A296908

Examples

			The base-10 digits of 1212 are 1,2,1,2; here #(pits) = 1 and #(peaks) = 1, so 1212 is in the sequence.
		

Links

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

Crossrefs

Cf. A296882, A296712, A296883, A296884.

Programs

Mathematica

z = 200; b = 10;
d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296882 *)
Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296883 *)
Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296884 *)

Extensions

Overview table corrected by Georg Fischer, Aug 24 2021