A296869 Numbers whose base-5 digits d(m), d(m-1), ..., d(0) have #(pits) < #(peaks); see Comments.

35, 36, 40, 41, 42, 45, 46, 47, 48, 65, 66, 67, 70, 71, 72, 73, 95, 96, 97, 98, 160, 161, 165, 166, 167, 170, 171, 172, 173, 175, 180, 181, 190, 191, 192, 195, 196, 197, 198, 200, 205, 206, 210, 211, 212, 220, 221, 222, 223, 225, 230, 231, 235, 236, 237, 240

Offset

1,1

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 A296867-A296869 partition the natural numbers. See the guides at A296882 and A296712.

Links

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

Example

The base-5 digits of 240 are 1,4,3,0; here #(pits) = 0 and #(peaks) = 1, so 240 is in the sequence.

Mathematica

z = 200; b = 5;
d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296867 *)
Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296868 *)
Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296869 *)
updnQ[n_]:=Total[Which[#[[1]]<#[[2]]>#[[3]], 1, #[[1]]>#[[2]]<#[[3]], -1, True, 0]&/@Partition[IntegerDigits[n, 5], 3, 1]]>0; Select[Range[ 250], updnQ] (* Harvey P. Dale, Dec 20 2020 *)

Crossrefs

Cf. A296882, A296712, A296867, A296868.

Sequence in context: A210320 A165856 A319484 * A099647 A064993 A041611

Adjacent sequences: A296866 A296867 A296868 * A296870 A296871 A296872

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 09 2018

Status

approved