A247632
Numbers k such that d(r,k) = 0 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
1, 4, 6, 12, 15, 21, 25, 29, 38, 42, 48, 52, 55, 60, 64, 66, 70, 72, 78, 83, 86, 89, 93, 96, 100, 102, 104, 107, 109, 111, 113, 119, 122, 130, 134, 136, 139, 144, 151, 153, 157, 159, 163, 166, 169, 173, 177, 179, 184, 187, 191, 195, 198, 202, 204, 209, 211
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 *)
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 *)
A247635
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
2, 8, 9, 10, 11, 14, 16, 17, 18, 20, 22, 24, 26, 28, 30, 31, 32, 33, 34, 35, 37, 39, 40, 43, 44, 45, 47, 49, 51, 54, 57, 58, 59, 62, 63, 67, 69, 73, 74, 75, 76, 79, 81, 82, 85, 87, 90, 92, 94, 97, 98, 106, 114, 115, 116, 117, 121, 123, 124, 125, 126, 128
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) = 2 and a(2) = 8.
-
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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