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A296882
Numbers whose base-10 digits d(m), d(m-1), ..., d(0) have #(pits) = #(peaks); see Comments.
69
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
1,2
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 #(pits) = #(peaks) #(pits) > #(peaks) #(pits) < #(peaks)
LINKS
EXAMPLE
The base-10 digits of 1212 are 1,2,1,2; here #(pits) = 1 and #(peaks) = 1, so 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
KEYWORD
nonn,base,easy
AUTHOR
Clark Kimberling, Jan 10 2018
EXTENSIONS
Overview table corrected by Georg Fischer, Aug 24 2021
STATUS
approved