A296905 Numbers whose base-20 digits d(m), d(m-1), ..., d(0) have #(pits) < #(peaks); see Comments.

440, 441, 460, 461, 462, 480, 481, 482, 483, 500, 501, 502, 503, 504, 520, 521, 522, 523, 524, 525, 540, 541, 542, 543, 544, 545, 546, 560, 561, 562, 563, 564, 565, 566, 567, 580, 581, 582, 583, 584, 585, 586, 587, 588, 600, 601, 602, 603, 604, 605, 606, 607

Offset: 1

Author

Clark Kimberling, Jan 12 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 A296903..A296905 partition the natural numbers. See the guides at A296712 and A296882.

Examples

			The base-20 digits of 176441 are 1,2,1,2,1; here #(pits) = 1 and #(peaks) = 2, so 176441 is in the sequence.
		

Links

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

Crossrefs

Cf. A296882, A296712, A296903, A296904.

Programs

Mathematica

z = 200; b = 20;
d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296903 *)
Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296904 *)
Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296905 *)

Extensions

b-file replaced by Clark Kimberling, Feb 27 2018