Clark Kimberling, <a href="/A246358/b246358_1.txt">Table of n, a(n) for n = 1..1000</a>

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Numbers k such that d(r,k) = 1 and d(s,k) = 0, where d(x,k) = kth k-th binary digit of x, r = {sqrt(2)}, s = {sqrt(3)}, and { } = fractional part.

Every positive integer lies in exactly one of these: A246356, A246357, A246358, 247356A247356.

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Numbers k such that d(r,k) = 1 and d(s,k) = 0, where d(x,k) = kth binary digit of x, r = {2*sqrt(2)}, s = {sqrt(3)}, and { } = fractional part.

2, 6, 12, 13, 18, 26, 29, 27, 31, 34, 35, 36, 39, 40, 43, 44, 48, 52, 66, 46, 50, 53, 65, 68, 71, 73, 77, 79, 80, 84, 87, 89, 93, 94, 96, 95, 97, 102, 104, 111, 113, 103, 110, 112, 114, 122, 118, 123, 124, 126, 130, 127, 132, 139, 133, 135, 142, 144, 143, 145, 151, 146, 152, 155, 159, 163, 166, 156, 160, 171, 174, 177, 179, 187, 191, 176, 180, 192, 195, 196, 202, 204, 197, 205, 206

Every positive integer lies in exactly one of these: A246356, A246357, A246358, A247356. Let s denote any of these; is lim(#s < n)/n = 1/4, where (#s < n) represents the number of numbers in s that are < n?

Every positive integer lies in exactly one of these: A246356, A246357, A246358, 247356.

Clark Kimberling, <a href="/A246358/b246358_1.txt">Table of n, a(n) for n = 1..1000</a>

{2*sqrt(2)} has binary digits 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1,0,0,...

{1*sqrt(3)} has binary digits 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0,1,1,..,

so that a(1) = 2 and a(2) = 13.

z = 200500; r = FractionalPart[Sqrt[2]]; s = FractionalPart[Sqrt[3]];

u = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[r, 2, z][[1]]

v = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[s, 2, z][[1]]

Numbers k such that d(r,k) = 1 and d(s,k) = 0, where d(x,k) = kth binary digit of x, r = {2*sqrt(2)}, s = {sqrt(3)}, and { } = fractional part.

Every positive integer lies in exactly one of these: A246356, A246357, A246358, A247356, and if . Let s denotes denote any of these, then ; is lim(#s < n)/n = 1/4, where (#s < n) represents the number of numbers in s that are < n.?

{2*sqrt(2)} has binary digits 1,1,0,1,0,1,0,0,0,0,0,1,0,0,...

{1*sqrt(3)} has binary digits 1,0,1,1,1,0,1,1,0,1,1,0,1,1,..,

approved

editing

proposed

approved

editing

proposed

Every positive integer lies in exactly one of these: A246356, A246357, A246358, 247356, A247356, and if s denotes any of these, then lim(#s < n)/n = 1/4, where (#s < n) represents the number of numbers in s that are < n.