

A296870


Numbers whose base6 digits d(m), d(m1), ..., d(0) have #(pits) = #(peaks); see Comments.


4



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, 42, 43, 44, 45, 46, 47, 50, 51, 52, 53, 57, 58, 59, 64, 65, 71, 72, 78, 79, 84, 85, 86, 87, 88, 89, 93, 94, 95, 100, 101
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OFFSET

1,2


COMMENTS

A pit is an index i such that d(i1) > d(i) < d(i+1); a peak is an index i such that d(i1) < d(i) > d(i+1). The sequences A296870A296872 partition the natural numbers. See the guides at A296882 and A296712.


LINKS



EXAMPLE

The base6 digits of 101 are 2,4,5; here #(pits) = 0 and #(peaks) = 0, so 101 is in the sequence.


MATHEMATICA

z = 200; b = 6;
d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
Select[Range [z], Count[d[#], 2] == Count[d[#], 2] &] (* A296870 *)
Select[Range [z], Count[d[#], 2] < Count[d[#], 2] &] (* A296871 *)
Select[Range [z], Count[d[#], 2] > Count[d[#], 2] &] (* A296872 *)


CROSSREFS



KEYWORD

nonn,base,easy


AUTHOR



STATUS

approved



