A296695 -id:A296695 - cp's OEIS frontend

A296712 Numbers whose base-10 digits d(m), d(m-1), ..., d(0) have #(rises) = #(falls); see Comments.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 102, 103, 104, 105, 106, 107, 108, 109, 111, 120, 121, 130, 131, 132, 140, 141, 142, 143, 150, 151, 152, 153, 154, 160, 161, 162, 163, 164, 165, 170, 171, 172, 173, 174, 175, 176, 180, 181

Offset: 1

Clark Kimberling, Jan 08 2018

A rise is an index i such that d(i) < d(i+1); a fall is an index i such that d(i) > d(i+1). The sequences A296712-A296714 partition the natural numbers.
****
Guide to related sequences:
Base   #(rises) = #(falls)   #(rises) > #(falls)   #(rises) < #(falls)
          A005408             (none)                A005843
          A296691             A296692               A296693
          A296694             A296695               A296696
          A296697             A296698               A296699
          A296700             A296701               A296702
          A296703             A296704               A296705
          A296706             A296707               A296708
          A296709             A296710               A296711
         A296712             A296713               A296714
         A296744             A296745               A296746
         A296747             A296748               A296749
         A296750             A296751               A296752
         A296753             A296754               A296755
         A296756             A296757               A296758
         A296759             A296760               A296761
         A296762             A296763               A296764
         A296765             A296766               A296767

			The base-10 digits of 181 are 1,8,1; here #(rises) = 1 and #(falls) = 1, so 181 is in the sequence.

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

Cf. A296713, A296714, A296712.

z = 200; b = 10; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296712 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296713 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296714 *)

A296694 Numbers whose base-4 digits d(m), d(m-1), ... d(0) have #(rises) = #(falls); see Comments.

Original entry on oeis.org

1, 2, 3, 5, 10, 15, 17, 18, 19, 21, 24, 25, 28, 29, 30, 33, 34, 35, 38, 39, 42, 44, 45, 46, 49, 50, 51, 54, 55, 59, 63, 65, 66, 67, 69, 74, 79, 81, 82, 83, 85, 88, 89, 92, 93, 94, 96, 101, 104, 105, 112, 117, 122, 124, 125, 126, 129, 130, 131, 133, 138, 143

Offset: 1

Clark Kimberling, Dec 21 2017

A rise is an index i such that d(i) < d(i+1); a fall is an index i such that d(i) > d(i+1). The sequences A296694-A296696 partition the natural numbers. See the guide at A296712.

			The base-4 digits of 143 are 2,0,3,3; here #(rises) = 1 and #(falls) = 1, so 143 is in the sequence.

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

Cf. A296695, A296696, A296700, A296712.

z = 200; b = 4; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296694 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296695 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296696 *)

A296696 Numbers whose base-4 digits d(m), d(m-1), ... d(0) have #(rises) < #(falls); see Comments.

Original entry on oeis.org

4, 8, 9, 12, 13, 14, 16, 20, 32, 36, 37, 40, 41, 48, 52, 53, 56, 57, 58, 60, 61, 62, 64, 68, 72, 73, 76, 77, 78, 80, 84, 100, 116, 120, 121, 128, 132, 136, 137, 140, 141, 142, 144, 145, 146, 147, 148, 149, 152, 153, 156, 157, 158, 160, 164, 165, 168, 169

Offset: 1

Clark Kimberling, Dec 21 2017

A rise is an index i such that d(i) < d(i+1); a fall is an index i such that d(i) > d(i+1). The sequences A296694-A296696 partition the natural numbers. See the guide at A296712.

			The base-4 digits of 196 are 3,0,1,0; here #(rises) = 1 and #(falls) = 2, so 196 is in the sequence.

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

Cf. A296694, A296695, A296712.

z = 200; b = 4; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296694 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296695 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296696 *)

Example corrected by Harvey P. Dale, Sep 04 2018

cp's OEIS Frontend

A296712 Numbers whose base-10 digits d(m), d(m-1), ..., d(0) have #(rises) = #(falls); see Comments.

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A296694 Numbers whose base-4 digits d(m), d(m-1), ... d(0) have #(rises) = #(falls); see Comments.

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A296696 Numbers whose base-4 digits d(m), d(m-1), ... d(0) have #(rises) < #(falls); see Comments.

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