cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-6 of 6 results.

A376357 Positions of numbers in A007961 that end in 0.

Original entry on oeis.org

4, 8, 9, 13, 16, 20, 24, 25, 29, 33, 34, 36, 40, 44, 45, 49, 53, 57, 58, 62, 64, 68, 72, 73, 77, 80, 81, 85, 89, 90, 94, 97, 100, 104, 108, 109, 113, 116, 120, 121, 125, 129, 130, 134, 137, 141, 144, 148, 152, 153, 157, 160, 164, 168, 169, 173, 177, 178, 182
Offset: 1

Views

Author

Clark Kimberling, Sep 25 2024

Keywords

Comments

Every positive integer is in exactly one of these sequences: this sequence, A376358, A376359, or A376360.
Conjecture: {a(n+1) - a(n) : n >= 1} = {1,2,3,4}. (See related conjectures at A376358-A376360.)

Crossrefs

Cf. A007961, A376354, A376358, A376359, A376360.

Programs

  • Mathematica
    a[n_, poly_] := FromDigits[FoldList[{Mod[#[[1]], #2], Quotient[#[[1]], #2]} &, {n, 0}, Reverse[Map[(poly - 2)  #  (# - 1)/2 + # &,
Range[Floor[Sqrt[2  n]]]]]][[All, 2]]]
t4 = Map[a[#, 4] &, Range[200]];  (* A007961 *)
m = Mod[t4, 10];
Table[Flatten[Position[m, r]], {r, 0, 2}]
p0 = Flatten[Position[m, 0]]  (* this sequence *)
p1 = Flatten[Position[m, 1]]  (* A376358 *)
p2 = Flatten[Position[m, 2]]  (* A376359 *)
p3 = Flatten[Position[m, 3]]  (* A376360 *)
(* Peter J. C. Moses, Sep 20 2024 *)

A376358 Positions of numbers in A007961 that end in 1.

Original entry on oeis.org

1, 5, 10, 14, 17, 21, 26, 30, 35, 37, 41, 46, 50, 54, 59, 63, 65, 69, 74, 78, 82, 86, 91, 95, 98, 101, 105, 110, 114, 117, 122, 126, 131, 135, 138, 142, 145, 149, 154, 158, 161, 165, 170, 174, 179, 183, 186, 190, 195, 197, 201, 206, 210, 213, 217, 222, 226
Offset: 1

Views

Author

Clark Kimberling, Sep 25 2024

Keywords

Comments

Every positive integer is in exactly one of these sequences: A376358, this sequence, A376359, or A376360.
Conjecture: {a(n+1) - a(n) : n >= 1} = {2,3,4,5,6,7}. (See related conjectures at A376357, A376359, and A376360.)

Crossrefs

Cf. A007961, A376354, A376357, A376359, A376360.

Programs

  • Mathematica
    a[n_, poly_] := FromDigits[FoldList[{Mod[#[[1]], #2], Quotient[#[[1]], #2]} &, {n, 0}, Reverse[Map[(poly - 2)  #  (# - 1)/2 + # &,
Range[Floor[Sqrt[2  n]]]]]][[All, 2]]]
t4 = Map[a[#, 4] &, Range[200]];  (* A007961 *)
m = Mod[t4, 10];
Table[Flatten[Position[m, r]], {r, 0, 2}]
p0 = Flatten[Position[m, 0]]  (* A376357 *)
p1 = Flatten[Position[m, 1]]  (* this sequence *)
p2 = Flatten[Position[m, 2]]  (* A376359 *)
p3 = Flatten[Position[m, 3]]  (* A376360 *)
(* Peter J. C. Moses, Sep 20 2024 *)

A376359 Positions of numbers in A007961 that end in 2.

Original entry on oeis.org

2, 6, 11, 15, 18, 22, 27, 31, 38, 42, 47, 51, 55, 60, 66, 70, 75, 79, 83, 87, 92, 96, 99, 102, 106, 111, 115, 118, 123, 127, 132, 136, 139, 143, 146, 150, 155, 159, 162, 166, 171, 175, 180, 184, 187, 191, 198, 202, 207, 211, 214, 218, 223, 227, 231, 236, 240
Offset: 1

Views

Author

Clark Kimberling, Sep 25 2024

Keywords

Comments

Every positive integer is in exactly one of these sequences: A376357, A376358, this sequence, or A376360.
Conjecture: {a(n+1) - a(n) : n >= 1} = {3,4,5,6,7,8,9,10}. (See related conjectures at A376357, A376358, and A376360.)

Crossrefs

Cf. A007961, A376354, A376357, A376358, A376360.

Programs

  • Mathematica
    a[n_, poly_] := FromDigits[FoldList[{Mod[#[[1]], #2], Quotient[#[[1]], #2]} &, {n, 0}, Reverse[Map[(poly - 2)  #  (# - 1)/2 + # &,
Range[Floor[Sqrt[2  n]]]]]][[All, 2]]]
t4 = Map[a[#, 4] &, Range[200]];  (* A007961 *)
m = Mod[t4, 10];
Table[Flatten[Position[m, r]], {r, 0, 2}]
p0 = Flatten[Position[m, 0]]  (* A376357 *)
p1 = Flatten[Position[m, 1]]  (* A376359 *)
p2 = Flatten[Position[m, 2]]  (* this sequence *)
p3 = Flatten[Position[m, 3]]  (* A376360 *)
(* Peter J. C. Moses, Sep 20 2024 *)

A376355 Numbers that end in 1 when written in base of triangular numbers (cf. A000462).

Original entry on oeis.org

1, 4, 7, 11, 14, 16, 19, 22, 25, 29, 32, 35, 37, 40, 43, 46, 49, 52, 56, 59, 62, 67, 70, 73, 77, 79, 82, 85, 89, 92, 95, 98, 102, 106, 109, 112, 116, 119, 121, 124, 127, 131, 134, 137, 140, 143, 147, 150, 152, 154, 157, 160, 164, 167, 169, 172, 175, 178, 182
Offset: 1

Views

Author

Clark Kimberling, Sep 22 2024

Keywords

Comments

Every positive integer is in exactly one of the following sequences: A376355, this sequence, or A376356.
Conjecture: {a(n+1) - a(n) : n >= 1} = {2,3,4,5,6}. (See related conjectures at A376354 and A376356.)

Crossrefs

Cf. A000462, A376354, A376356, A376357.

Programs

  • Mathematica
    a[n_, poly_] := FromDigits[FoldList[{Mod[#[[1]], #2], Quotient[#[[1]], #2]} &, {n, 0}, Reverse[Map[(poly - 2)  #  (# - 1)/2 + # &, Range[Floor[Sqrt[2  n]]]]]][[All, 2]]]
t3 = Map[a[#, 3] &, Range[200]]; (* A000462 *)
m = Mod[t3, 10]
Table[Flatten[Position[m, r]], {r, 0, 2}]
p0 = Flatten[Position[m, 0]]  (* A376354 *)
p1 = Flatten[Position[m, 1]]  (* this sequence *)
p2 = Flatten[Position[m, 2]]  (* A376356 *)
(* Peter J. C. Moses, Sep 20 2024 *)

A376360 Positions of numbers in A007961 that end in 3.

Original entry on oeis.org

3, 7, 12, 19, 23, 28, 32, 39, 43, 48, 52, 56, 61, 67, 71, 76, 84, 88, 93, 103, 107, 112, 119, 124, 128, 133, 140, 147, 151, 156, 163, 167, 172, 176, 181, 188, 192, 199, 203, 208, 215, 219, 224, 228, 232, 237, 244, 248, 253, 259, 263, 268, 275, 279, 284, 288
Offset: 1

Views

Author

Clark Kimberling, Sep 25 2024

Keywords

Comments

Every positive integer is in exactly one of these sequences: A376357, A376358, A376359, or this sequence.
Conjecture: {a(n+1) - a(n) : n >= 1} = {4,5,6,7,8,9,10,11,13}. It has been checked that a(n+1) - a(n) is not 12 for 1<=n<=300000. (See related conjectures at A376357, A376358, and A376359.)

Crossrefs

Cf. A007961, A376354, A376357, A376358, A376359.

Programs

  • Mathematica
    a[n_, poly_] := FromDigits[FoldList[{Mod[#[[1]], #2], Quotient[#[[1]], #2]} &, {n, 0}, Reverse[Map[(poly - 2)  #  (# - 1)/2 + # &,
Range[Floor[Sqrt[2  n]]]]]][[All, 2]]]
t4 = Map[a[#, 4] &, Range[200]];  (* A007961 *)
m = Mod[t4, 10];
Table[Flatten[Position[m, r]], {r, 0, 2}]
p0 = Flatten[Position[m, 0]]  (* A376357 *)
p1 = Flatten[Position[m, 1]]  (* A376358 *)
p2 = Flatten[Position[m, 2]]  (* A376359 *)
p3 = Flatten[Position[m, 3]]  (* this sequence *)
(* Peter J. C. Moses, Sep 20 2024 *)

A376356 Positions of numbers in A000462 that end in 2.

Original entry on oeis.org

2, 5, 8, 12, 17, 20, 23, 26, 30, 33, 38, 41, 44, 47, 50, 53, 57, 60, 63, 68, 71, 74, 80, 83, 86, 90, 93, 96, 99, 103, 107, 110, 113, 117, 122, 125, 128, 132, 138, 141, 144, 148, 155, 158, 161, 165, 170, 173, 176, 179, 183, 188, 192, 195, 198
Offset: 1

Views

Author

Clark Kimberling, Sep 25 2024

Keywords

Comments

Every positive integer is in exactly one of the following sequences: A376354, A376355, or this sequence.
Conjecture: {a(n+1) - a(n) : n >= 1} = {3,4,5,6,7,8,9}. (See related conjectures at A376354 and A376355.)

Crossrefs

Cf. A000462, A376354, A376355, A376357.

Programs

  • Mathematica
    a[n_, poly_] := FromDigits[FoldList[{Mod[#[[1]], #2], Quotient[#[[1]], #2]} &, {n, 0}, Reverse[Map[(poly - 2)  #  (# - 1)/2 + # &, Range[Floor[Sqrt[2  n]]]]]][[All, 2]]]
t3 = Map[a[#, 3] &, Range[200]]; (* A000462 *)
m = Mod[t3, 10]
Table[Flatten[Position[m, r]], {r, 0, 2}]
p0 = Flatten[Position[m, 0]]  (* A376354 *)
p1 = Flatten[Position[m, 1]]  (* A376355 *)
p2 = Flatten[Position[m, 2]]  (* this sequence *)
(* Peter J. C. Moses, Sep 20 2024 *)
Showing 1-6 of 6 results.

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