A247455
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 = {3*sqrt(2)}, and { } = fractional part.
Original entry on oeis.org
1, 8, 9, 10, 11, 15, 21, 25, 29, 38, 42, 48, 51, 54, 57, 58, 59, 62, 64, 66, 70, 72, 78, 81, 82, 86, 89, 93, 96, 107, 109, 111, 113, 122, 128, 130, 134, 136, 139, 144, 147, 148, 149, 151, 153, 161, 162, 165, 169, 173, 181, 182, 183, 187, 191, 195, 200, 202
Offset: 1
{1*sqrt(2)} has binary digits 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1,...
{3*sqrt(2)} has binary digits 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1,...
so that a(1) = 2 and a(2) = 8.
-
z = 400; r = FractionalPart[Sqrt[2]]; s = FractionalPart[3*Sqrt[2]];
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]] (* A247455 *)
Flatten[Position[t2, 1]] (* A247456 *)
Flatten[Position[t3, 1]] (* A247457 *)
Flatten[Position[t4, 1]] (* A247458 *)
A247456
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 = {3*sqrt(2)}, and { } = fractional part.
Original entry on oeis.org
4, 6, 12, 14, 20, 24, 28, 37, 47, 52, 55, 60, 63, 69, 83, 85, 92, 100, 102, 104, 106, 119, 121, 129, 150, 157, 159, 163, 166, 168, 177, 179, 184, 186, 190, 198, 201, 215, 219, 228, 232, 236, 241, 246, 250, 252, 254, 256, 258, 271, 276, 284, 288, 303, 305
Offset: 1
{1*sqrt(2)} has binary digits 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1,...
{3*sqrt(2)} has binary digits 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1,...
so that a(1) = 4 and a(2) = 6.
-
z = 400; r = FractionalPart[Sqrt[2]]; s = FractionalPart[3*Sqrt[2]];
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]] (* A247455 *)
Flatten[Position[t2, 1]] (* A247456 *)
Flatten[Position[t3, 1]] (* A247457 *)
Flatten[Position[t4, 1]] (* A247458 *)
A247458
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 = {3*sqrt(2)}, and { } = fractional part.
Original entry on oeis.org
3, 5, 7, 13, 16, 17, 19, 23, 27, 30, 31, 32, 33, 34, 36, 39, 40, 43, 44, 46, 50, 53, 56, 61, 68, 73, 74, 75, 76, 80, 84, 87, 91, 94, 97, 99, 101, 103, 105, 114, 115, 116, 118, 120, 123, 124, 125, 127, 131, 132, 137, 140, 141, 142, 146, 154, 156, 158, 160
Offset: 1
{1*sqrt(2)} has binary digits 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1,...
{3*sqrt(2)} has binary digits 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1,...
so that a(1) = 3 and a(2) = 5.
-
z = 400; r = FractionalPart[Sqrt[2]]; s = FractionalPart[3*Sqrt[2]];
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]] (* A247455 *)
Flatten[Position[t2, 1]] (* A247456 *)
Flatten[Position[t3, 1]] (* A247457 *)
Flatten[Position[t4, 1]] (* A247458 *)
Showing 1-3 of 3 results.
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