A151821 -id:A151821 - cp's OEIS frontend

A179461 Decimal expansion of sqrt(51)/7.

1, 0, 2, 0, 2, 0, 4, 0, 6, 1, 2, 2, 0, 4, 0, 7, 1, 4, 2, 5, 7, 1, 3, 4, 2, 8, 3, 0, 1, 9, 5, 3, 2, 3, 6, 1, 1, 2, 5, 2, 3, 1, 0, 1, 6, 5, 7, 0, 0, 3, 9, 0, 5, 4, 7, 6, 0, 1, 2, 0, 4, 4, 1, 1, 8, 2, 3, 6, 8, 8, 6, 2, 9, 4, 9, 1, 4, 3, 1, 6, 9, 8, 0, 3, 6, 9, 9, 8, 3, 1, 6, 2, 1, 8, 9, 7, 4, 3, 4, 5, 4, 6, 2, 0, 6

Offset: 1

Mark Dols, Jul 14 2010

sqrt(3/2)= sqrt(12/8)= 1.224744... sqrt(51/49)= sqrt(102/98)= 1.0202040612... sqrt (501/499)=sqrt (1002/998)= 1.002002004...

Cf. A063886, A115754, A000984, A151821.

RealDigits[ Sqrt@ 51/7, 10, 111][[1]] (* Robert G. Wilson v, Aug 23 2010 *)

sqrt(51)/7 \\ Charles R Greathouse IV, Apr 25 2016

Keyword:frac replaced by keyword:cons - R. J. Mathar, Jul 20 2010

More terms from Robert G. Wilson v, Aug 23 2010

A384543 Number of distinct values from the bitwise operation i XOR j for all integers i and j in the range [1, n].

Original entry on oeis.org

1, 2, 4, 7, 8, 8, 8, 15, 16, 16, 16, 16, 16, 16, 16, 31, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 63, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 127, 128, 128

Offset: 1

Darío Clavijo, Jun 02 2025

For any n, the maximum value of (i XOR j) is < 2^floor(log_2(n))+1.

			For n=3, a(3) = 4 because:
 i | j | i XOR j
---+---+-------
 1 | 1 | 0
 1 | 2 | 3
 1 | 3 | 2
 2 | 1 | 3
 2 | 2 | 0
 2 | 3 | 1
 3 | 1 | 2
 3 | 2 | 1
 3 | 3 | 0
In total there are 4 unique values for i XOR j.

Cf. A000079, A000225, A070939, A151821.

a[n_] := CountDistinct[Flatten[Table[BitXor[i, j], {i, 1, n}, {j, 1, i}]]]; Array[a, 100] (* Amiram Eldar, Jun 02 2025 *)

a(n) = #setbinop((x,y)->bitxor(x,y), [1..n]); \\ Michel Marcus, Jun 02 2025

def a(n):
    if n < 4: return [1,1,2,4][n]
    k2 = 1 << n.bit_length()
    if (n & (n - 1)) == 0: return k2 - 1
    return k2
print([a(n) for n in range(1, 68)])

a(2^k) = A000225(k+1) for k > 1.
a(2^k-1) = A151821(k).
a(2^k+1) = A000079(k+1).
a(n) = 2^k if 2^(k-1) < n < 2^k with k=2^floor(log_2(n))+1.

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A179461 Decimal expansion of sqrt(51)/7.

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