A296712 -id:A296712 - cp's OEIS frontend

A296862 Numbers whose base-3 digits d(m), d(m-1), ..., d(0) have #(pits) > #(peaks); see Comments.

10, 11, 19, 20, 23, 31, 32, 35, 37, 38, 58, 59, 62, 64, 65, 71, 73, 74, 77, 91, 92, 93, 94, 95, 98, 100, 101, 104, 105, 106, 107, 112, 113, 116, 118, 119, 154, 155, 158, 172, 173, 174, 175, 176, 179, 181, 182, 185, 186, 187, 188, 193, 194, 197, 199, 200, 208

Offset: 1

Clark Kimberling, Jan 09 2018

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 A296861-A296863 partition the natural numbers. See the guides at A296882 and A296712.

			The base-3 digits of 208 are 2, 1, 2, 0, 1; here #(pits) = 2 and #(peaks) = 1, so 208 is in the sequence.

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

Cf. A296882, A296712, A296861, A296863.

z = 200; b = 3;
d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296861 *)
Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296862 *)
Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296863 *)

A296863 Numbers whose base-3 digits d(m), d(m-1), ..., d(0) have #(pits) < #(peaks); see Comments.

Original entry on oeis.org

15, 16, 42, 43, 45, 48, 49, 84, 87, 88, 123, 124, 126, 129, 130, 135, 136, 137, 138, 141, 142, 144, 147, 148, 149, 150, 151, 165, 168, 169, 204, 205, 246, 249, 250, 252, 258, 259, 261, 264, 265, 327, 330, 331, 366, 367, 369, 372, 373, 378, 379, 380, 381, 384

Offset: 1

Clark Kimberling, Jan 09 2018

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 A296861-A296863 partition the natural numbers. See the guides at A296882 and A296712.

			The base-3 digits of 384 are 1, 1, 2, 0, 2, 0; here #(pits) = 1 and #(peaks) = 2, so 384 is in the sequence.

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

Cf. A296882, A296712, A296861, A296862.

z = 200; b = 3;
d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296861 *)
Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296862 *)
Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296863 *)

A296864 Numbers whose base-4 digits d(m), d(m-1), ..., d(0) have #(pits) = #(peaks); see Comments.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 20, 21, 22, 23, 26, 27, 31, 32, 36, 37, 40, 41, 42, 43, 47, 48, 52, 53, 56, 57, 58, 60, 61, 62, 63, 64, 65, 66, 67, 68, 72, 73, 76, 77, 78, 80, 84, 85, 86, 87, 90, 91, 95, 97, 98, 99, 102, 103, 104, 105

Offset: 1

Clark Kimberling, Jan 09 2018

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 A296864-A296866 partition the natural numbers. See the guides at A296882 and A296712.

			The base-4 digits of 105 are 1, 2, 2, 1; here #(pits) = 0 and #(peaks) = 0, so 105 is in the sequence.

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

Cf. A296882, A296712, A296865, A296866.

z = 200; b = 4;
d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296864 *)
Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296865 *)
Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296866 *)

A296865 Numbers whose base-4 digits d(m), d(m-1), ..., d(0) have #(pits) > #(peaks); see Comments.

Original entry on oeis.org

17, 18, 19, 33, 34, 35, 38, 39, 49, 50, 51, 54, 55, 59, 69, 70, 71, 74, 75, 79, 81, 82, 83, 133, 134, 135, 138, 139, 143, 145, 146, 147, 154, 155, 159, 161, 162, 163, 166, 167, 197, 198, 199, 202, 203, 207, 209, 210, 211, 218, 219, 223, 225, 226, 227, 230

Offset: 1

Clark Kimberling, Jan 09 2018

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 A296864-A296866 partition the natural numbers. See the guides at A296882 and A296712.

			The base-4 digits of 230 are 3, 2, 1, 2; here #(pits) = 1 and #(peaks) = 0, so 230 is in the sequence.

Clark Kimberling, Table of n, a(n) for n = 1..9999

Cf. A296882, A296712, A296864, A296866.

z = 200; b = 4;
d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296864 *)
Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296865 *)
Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296866 *)

A296866 Numbers whose base-4 digits d(m), d(m-1), ..., d(0) have #(pits) < #(peaks); see Comments.

Original entry on oeis.org

24, 25, 28, 29, 30, 44, 45, 46, 88, 89, 92, 93, 94, 96, 100, 101, 108, 109, 110, 112, 116, 117, 120, 121, 122, 172, 173, 174, 176, 180, 181, 184, 185, 186, 260, 264, 265, 268, 269, 270, 344, 345, 348, 349, 350, 352, 356, 357, 364, 365, 366, 368, 372, 373

Offset: 1

Clark Kimberling, Jan 09 2018

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 A296864-A296866 partition the natural numbers. See the guides at A296882 and A296712.

			The base-4 digits of 373 are 1,1,3,1,1; here #(pits) = 0 and #(peaks) = 2, so 373 is in the sequence.

Clark Kimberling, Table of n, a(n) for n = 1..9999

Cf. A296882, A296712, A296864, A296865.

z = 200; b = 4;
d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296864 *)
Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296865 *)
Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296866 *)

A296867 Numbers whose base-5 digits d(m), d(m-1), ..., d(0) have #(pits) = #(peaks); see Comments.

Original entry on oeis.org

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, 30, 31, 32, 33, 34, 37, 38, 39, 43, 44, 49, 50, 55, 56, 60, 61, 62, 63, 64, 68, 69, 74, 75, 80, 81, 85, 86, 87, 90, 91, 92, 93, 94, 99, 100, 105, 106, 110, 111, 112

Offset: 1

Clark Kimberling, Jan 09 2018

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.

			The base-5 digits of 112 are 4,2,2; here #(pits) = 0 and #(peaks) = 0, so 112 is in the sequence.

Clark Kimberling, Table of n, a(n) for n = 1..9999

Cf. A296882, A296712, A296868, A296869.

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 *)

A296868 Numbers whose base-5 digits d(m), d(m-1), ..., d(0) have #(pits) > #(peaks); see Comments.

Original entry on oeis.org

26, 27, 28, 29, 51, 52, 53, 54, 57, 58, 59, 76, 77, 78, 79, 82, 83, 84, 88, 89, 101, 102, 103, 104, 107, 108, 109, 113, 114, 119, 131, 132, 133, 134, 137, 138, 139, 143, 144, 149, 151, 152, 153, 154, 256, 257, 258, 259, 262, 263, 264, 268, 269, 274, 276, 277

Offset: 1

Clark Kimberling, Jan 09 2018

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.

			The base-5 digits of 277 are 2,1,0,2; here #(pits) = 1 and #(peaks) = 0, so 277 is in the sequence.

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

Cf. A296882, A296712, A296867, A296869.

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 *)

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

Original entry on oeis.org

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

Clark Kimberling, Jan 09 2018

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.

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

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

Cf. A296882, A296712, A296867, A296868.

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 *)

A296870 Numbers whose base-6 digits d(m), d(m-1), ..., d(0) have #(pits) = #(peaks); see Comments.

Original entry on oeis.org

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, 42, 43, 44, 45, 46, 47, 50, 51, 52, 53, 57, 58, 59, 64, 65, 71, 72, 78, 79, 84, 85, 86, 87, 88, 89, 93, 94, 95, 100, 101

Offset: 1

Clark Kimberling, Jan 09 2018

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 A296870-A296872 partition the natural numbers. See the guides at A296882 and A296712.

			The base-6 digits of 101 are 2,4,5; here #(pits) = 0 and #(peaks) = 0, so 101 is in the sequence.

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

Cf. A296882, A296712, A296871, A296872.

z = 200; b = 6;
d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296870 *)
Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296871 *)
Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296872 *)

A296871 Numbers whose base-6 digits d(m), d(m-1), ..., d(0) have #(pits) > #(peaks); see Comments.

Original entry on oeis.org

37, 38, 39, 40, 41, 73, 74, 75, 76, 77, 80, 81, 82, 83, 109, 110, 111, 112, 113, 116, 117, 118, 119, 123, 124, 125, 145, 146, 147, 148, 149, 152, 153, 154, 155, 159, 160, 161, 166, 167, 181, 182, 183, 184, 185, 188, 189, 190, 191, 195, 196, 197, 202, 203

Offset: 1

Clark Kimberling, Jan 09 2018

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 A296870-A296872 partition the natural numbers. See the guides at A296882 and A296712.

			The base-6 digits of 203 are 5,3,5; here #(pits) = 1 and #(peaks) = 0, so 203 is in the sequence.

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

Cf. A296882, A296712, A296870, A296872.

z = 200; b = 6;
d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296870 *)
Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296871 *)
Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296872 *)

cp's OEIS Frontend

A296862 Numbers whose base-3 digits d(m), d(m-1), ..., d(0) have #(pits) > #(peaks); see Comments.

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A296863 Numbers whose base-3 digits d(m), d(m-1), ..., d(0) have #(pits) < #(peaks); see Comments.

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A296864 Numbers whose base-4 digits d(m), d(m-1), ..., d(0) have #(pits) = #(peaks); see Comments.

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A296865 Numbers whose base-4 digits d(m), d(m-1), ..., d(0) have #(pits) > #(peaks); see Comments.

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A296866 Numbers whose base-4 digits d(m), d(m-1), ..., d(0) have #(pits) < #(peaks); see Comments.

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A296867 Numbers whose base-5 digits d(m), d(m-1), ..., d(0) have #(pits) = #(peaks); see Comments.

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A296868 Numbers whose base-5 digits d(m), d(m-1), ..., d(0) have #(pits) > #(peaks); see Comments.

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

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