A376359 -id:A376359 - cp's OEIS frontend

A376357 Positions of numbers in A007961 that end in 0.

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

Clark Kimberling, Sep 25 2024

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.)

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

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

Clark Kimberling, Sep 25 2024

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.)

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

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 *)

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

Clark Kimberling, Sep 25 2024

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.)

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

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 *)

cp's OEIS Frontend

A376357 Positions of numbers in A007961 that end in 0.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

A376358 Positions of numbers in A007961 that end in 1.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

A376360 Positions of numbers in A007961 that end in 3.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica