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A296882 Numbers n whose base-10 digits d(m), d(m-1), ..., d(0) have #(pits) = #(peaks); see Comments. 68
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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.

.

Guide to related sequences:

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

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               A296883

10           A296882             A296883               A296885

11           A296885             A296886               A296888

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

LINKS

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

EXAMPLE

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

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 *)

CROSSREFS

Cf. A296882, A296712, A296883, A296884.

Sequence in context: A258071 A266279 A296879 * A296885 A296888 A296891

Adjacent sequences:  A296879 A296880 A296881 * A296883 A296884 A296885

KEYWORD

nonn,base,easy

AUTHOR

Clark Kimberling, Jan 10 2018

STATUS

approved

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Last modified November 22 16:26 EST 2019. Contains 329396 sequences. (Running on oeis4.)