A283772 -id:A283772 - cp's OEIS frontend

A283773 Numbers k such that U(k) = 1 mod 3, where U = A001950 = upper Wythoff sequence.

3, 4, 5, 11, 12, 13, 19, 20, 27, 28, 35, 36, 42, 43, 44, 50, 51, 52, 58, 59, 60, 66, 67, 68, 74, 75, 82, 83, 90, 91, 97, 98, 99, 105, 106, 107, 113, 114, 115, 121, 122, 123, 129, 130, 137, 138, 144, 145, 146, 152, 153, 154, 160, 161, 162, 168, 169, 170, 176

Offset: 1

Clark Kimberling, Mar 18 2017

The sequences A283772, A283773, A283774 partition the positive integers.

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

Cf. A000201, A001622, A283772, A283774.

r = GoldenRatio^2; z = 350; t = Table[Floor[n*r], {n, 1, z}]; u = Mod[t, 3];
Flatten[Position[u, 0]]  (* A283772 *)
Flatten[Position[u, 1]]  (* A283773 *)
Flatten[Position[u, 2]]  (* A283774 *)

r = (3 + sqrt(5))/2;
for(n=1, 351, if(floor(n*r)%3==1, print1(n,", "))) \\ Indranil Ghosh, Mar 19 2017

import math
from sympy import sqrt
r = (3 + sqrt(5))/2
[n for n in range(1, 351) if int(math.floor(n*r))%3==1] # Indranil Ghosh, Mar 19 2017

a(n+1) - a(n) is in {1,6,7} for every n.

A283774 Numbers k such that U(k) == 2 mod 3, where U = A001950 = upper Wythoff sequence.

Original entry on oeis.org

1, 2, 8, 9, 10, 16, 17, 18, 24, 25, 26, 32, 33, 34, 40, 41, 48, 49, 55, 56, 57, 63, 64, 65, 71, 72, 73, 79, 80, 81, 87, 88, 89, 95, 96, 103, 104, 110, 111, 112, 118, 119, 120, 126, 127, 128, 134, 135, 136, 142, 143, 150, 151, 158, 159, 165, 166, 167, 173

Offset: 1

Clark Kimberling, Mar 19 2017

The sequences A283772, A283773, A283774 partition the positive integers.

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

Cf. A000201, A001622, A283772, A283774.

r = GoldenRatio^2; z = 350; t = Table[Floor[n*r], {n, 1, z}]; u = Mod[t, 3];
Flatten[Position[u, 0]]  (* A283772 *)
Flatten[Position[u, 1]]  (* A283773 *)
Flatten[Position[u, 2]]  (* A283774 *)

r = (3 + sqrt(5))/2;
for(n=1, 351, if(floor(n*r)%3==2, print1(n, ", "))) \\ Indranil Ghosh, Mar 21 2017

import math
from sympy import sqrt
r = (3 + sqrt(5))/2
[n for n in range(1, 351) if int(math.floor(n*r))%3==2] # Indranil Ghosh, Mar 21 2017

a(n+1) - a(n) is in {1,6,7} for every n.

cp's OEIS Frontend

A283773 Numbers k such that U(k) = 1 mod 3, where U = A001950 = upper Wythoff sequence.

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