A247631
Numbers k such that d(r,k) = 0 and d(s,k) = 0, where d(x,k) = k-th binary digit of x, r = {sqrt(2)}, s = {sqrt(8)}, and { } = fractional part.
Original entry on oeis.org
8, 9, 10, 11, 14, 20, 24, 28, 37, 47, 51, 54, 57, 58, 59, 62, 63, 69, 81, 82, 85, 92, 106, 121, 128, 129, 147, 148, 149, 150, 161, 162, 165, 168, 181, 182, 183, 186, 190, 200, 201, 214, 217, 218, 219, 225, 226, 227, 228, 232, 236, 241, 245, 248, 249, 258
Offset: 1
r has binary digits 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, ...
s has binary digits 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, ...
so that a(1) = 8 and a(2) = 9.
-
z = 400; r = FractionalPart[Sqrt[2]]; s = FractionalPart[Sqrt[8]];
u = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[r, 2, z]]
v = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[s, 2, z]]
t1 = Table[If[u[[n]] == 0 && v[[n]] == 0, 1, 0], {n, 1, z}];
t2 = Table[If[u[[n]] == 0 && v[[n]] == 1, 1, 0], {n, 1, z}];
t3 = Table[If[u[[n]] == 1 && v[[n]] == 0, 1, 0], {n, 1, z}];
t4 = Table[If[u[[n]] == 1 && v[[n]] == 1, 1, 0], {n, 1, z}];
Flatten[Position[t1, 1]] (* A247631 *)
Flatten[Position[t2, 1]] (* A247632 *)
Flatten[Position[t3, 1]] (* A247633 *)
Flatten[Position[t4, 1]] (* A247634 *)
A247633
Numbers k such that d(r,k) = 1 and d(s,k) = 0, where d(x,k) = k-th binary digit of x, r = {sqrt(2)}, s = {sqrt(8)}, and { } = fractional part.
Original entry on oeis.org
3, 5, 7, 13, 19, 23, 27, 36, 41, 46, 50, 53, 56, 61, 65, 68, 71, 77, 80, 84, 88, 91, 95, 99, 101, 103, 105, 108, 110, 112, 118, 120, 127, 133, 135, 138, 143, 146, 152, 156, 158, 160, 164, 167, 172, 176, 178, 180, 185, 189, 194, 197, 199, 203, 208, 210, 213
Offset: 1
r has binary digits 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, ...
s has binary digits 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, ...
so that a(1) = 1 and a(2) = 4.
-
z = 400; r = FractionalPart[Sqrt[2]]; s = FractionalPart[Sqrt[8]];
u = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[r, 2, z]]
v = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[s, 2, z]]
t1 = Table[If[u[[n]] == 0 && v[[n]] == 0, 1, 0], {n, 1, z}];
t2 = Table[If[u[[n]] == 0 && v[[n]] == 1, 1, 0], {n, 1, z}];
t3 = Table[If[u[[n]] == 1 && v[[n]] == 0, 1, 0], {n, 1, z}];
t4 = Table[If[u[[n]] == 1 && v[[n]] == 1, 1, 0], {n, 1, z}];
Flatten[Position[t1, 1]] (* A247631 *)
Flatten[Position[t2, 1]] (* A247632 *)
Flatten[Position[t3, 1]] (* A247633 *)
Flatten[Position[t4, 1]] (* A247634 *)
A247634
Numbers k such that d(r,k) = 1 and d(s,k) = 1, where d(x,k) = k-th binary digit of x, r = {sqrt(2)}, s = {sqrt(8)}, and { } = fractional part.
Original entry on oeis.org
2, 16, 17, 18, 22, 26, 30, 31, 32, 33, 34, 35, 39, 40, 43, 44, 45, 49, 67, 73, 74, 75, 76, 79, 87, 90, 94, 97, 98, 114, 115, 116, 117, 123, 124, 125, 126, 131, 132, 137, 140, 141, 142, 145, 154, 155, 170, 171, 174, 175, 188, 192, 193, 196, 205, 206, 207, 212
Offset: 1
r has binary digits 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, ...
s has binary digits 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, ...
so that a(1) = 1 and a(2) = 4.
-
z = 400; r = FractionalPart[Sqrt[2]]; s = FractionalPart[Sqrt[8]];
u = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[r, 2, z]]
v = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[s, 2, z]]
t1 = Table[If[u[[n]] == 0 && v[[n]] == 0, 1, 0], {n, 1, z}];
t2 = Table[If[u[[n]] == 0 && v[[n]] == 1, 1, 0], {n, 1, z}];
t3 = Table[If[u[[n]] == 1 && v[[n]] == 0, 1, 0], {n, 1, z}];
t4 = Table[If[u[[n]] == 1 && v[[n]] == 1, 1, 0], {n, 1, z}];
Flatten[Position[t1, 1]] (* A247631 *)
Flatten[Position[t2, 1]] (* A247632 *)
Flatten[Position[t3, 1]] (* A247633 *)
Flatten[Position[t4, 1]] (* A247634 *)
A247636
Numbers k such that d(r,k) != d(s,k), where d(x,k) = k-th binary digit of x, r = {sqrt(2)}, s = {sqrt(8)}, and { } = fractional part.
Original entry on oeis.org
1, 3, 4, 5, 6, 7, 12, 13, 15, 19, 21, 23, 25, 27, 29, 36, 38, 41, 42, 46, 48, 50, 52, 53, 55, 56, 60, 61, 64, 65, 66, 68, 70, 71, 72, 77, 78, 80, 83, 84, 86, 88, 89, 91, 93, 95, 96, 99, 100, 101, 102, 103, 104, 105, 107, 108, 109, 110, 111, 112, 113, 118
Offset: 1
r has binary digits 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, ...
s has binary digits 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, ...
so that a(1) = 1 and a(2) = 3.
-
z = 200; r = FractionalPart[Sqrt[2]]; s = FractionalPart[Sqrt[8]];
u = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[r, 2, z]];
v = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[s, 2, z]];
t = Table[If[u[[n]] == v[[n]], 1, 0], {n, 1, z}];
Flatten[Position[t, 1]] (* A247635 *)
Flatten[Position[t, 0]] (* A247636 *)
Showing 1-4 of 4 results.
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