A296894 - OEIS

A296894

Numbers whose base-14 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

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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 A296894-A296897 partition the natural numbers. See the guides at A296712 and A296882.

LINKS

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

EXAMPLE

The base-14 digits of 3152 are 1,2,1,2; here #(pits) = 1 and #(peaks) = 1, so 3152 is in the sequence.

MATHEMATICA

z = 200; b = 14;

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

Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &] (* A296894 *)

Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &] (* A296895 *)

Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &] (* A296896 *)

CROSSREFS

Cf. A296882, A296712, A296895, A296896.