A246356
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(3)}, and { } = fractional part.
Original entry on oeis.org
6, 9, 12, 20, 24, 28, 29, 37, 48, 52, 57, 58, 62, 66, 69, 81, 82, 89, 93, 96, 102, 104, 106, 111, 113, 122, 129, 130, 139, 144, 149, 151, 159, 161, 163, 165, 166, 177, 179, 181, 186, 187, 190, 191, 195, 201, 202, 204, 217, 219, 220, 222, 225, 228, 232, 233
Offset: 1
{sqrt(2)} has binary digits 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1,...
{sqrt(3)} has binary digits 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0,..
so that a(1) = 6.
-
z = 500; r = FractionalPart[Sqrt[2]]; s = FractionalPart[Sqrt[3]];
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]] (* A246356 *)
Flatten[Position[t2, 1]] (* A246357 *)
Flatten[Position[t3, 1]] (* A246358 *)
Flatten[Position[t4, 1]] (* A247356 *)
A246357
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(3)}, and { } = fractional part.
Original entry on oeis.org
1, 4, 8, 10, 11, 14, 15, 21, 25, 38, 42, 47, 51, 54, 55, 59, 60, 63, 64, 70, 72, 78, 83, 85, 86, 92, 100, 107, 109, 119, 121, 128, 134, 136, 147, 148, 150, 153, 157, 162, 168, 169, 173, 182, 183, 184, 198, 200, 209, 211, 214, 215, 218, 226, 227, 229, 241
Offset: 1
{sqrt(2)} has binary digits 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1,...
{sqrt(3)} has binary digits 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0,..
so that a(1) = 1 and a(2) = 4.
-
z = 500; r = FractionalPart[Sqrt[2]]; s = FractionalPart[Sqrt[3]];
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]] (* A246356 *)
Flatten[Position[t2, 1]] (* A246357 *)
Flatten[Position[t3, 1]] (* A246358 *)
Flatten[Position[t4, 1]] (* A247356 *)
A247356
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(3)}, and { } = fractional part.
Original entry on oeis.org
3, 5, 7, 16, 17, 19, 22, 23, 30, 32, 33, 41, 45, 49, 56, 61, 67, 74, 75, 76, 88, 90, 91, 98, 99, 101, 105, 108, 115, 116, 117, 120, 125, 131, 137, 138, 140, 141, 154, 158, 164, 167, 170, 172, 175, 178, 185, 188, 189, 193, 194, 199, 203, 221, 230, 231, 234
Offset: 1
{sqrt(2)} has binary digits 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1,...
{sqrt(3)} has binary digits 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0,..
so that a(1) = 3 and a(2) = 5.
-
z = 500; r = FractionalPart[Sqrt[2]]; s = FractionalPart[Sqrt[3]];
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]] (* A246356 *)
Flatten[Position[t2, 1]] (* A246357 *)
Flatten[Position[t3, 1]] (* A246358 *)
Flatten[Position[t4, 1]] (* A247356 *)
Showing 1-3 of 3 results.
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