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

Author

Clark Kimberling, Jan 09 2018

Keywords

• nonn
• base
• easy

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.

Examples

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

Links

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

Crossrefs

Cf. A296882, A296712, A296867, A296868.

Programs

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 *)