A003987 -id:A003987 - cp's OEIS frontend

A286150 Square array read by antidiagonals: A(n,k) = T(n XOR k, min(n,k)), where T(n,k) is sequence A001477 considered as a two-dimensional table, and XOR is bitwise-xor (A003987).

0, 2, 2, 5, 1, 5, 9, 13, 13, 9, 14, 8, 3, 8, 14, 20, 26, 7, 7, 26, 20, 27, 19, 42, 6, 42, 19, 27, 35, 43, 52, 62, 62, 52, 43, 35, 44, 34, 25, 51, 10, 51, 25, 34, 44, 54, 64, 33, 41, 16, 16, 41, 33, 64, 54, 65, 53, 88, 32, 23, 15, 23, 32, 88, 53, 65, 77, 89, 102, 116, 31, 39, 39, 31, 116, 102, 89, 77, 90, 76, 63, 101, 148, 30, 21, 30, 148, 101, 63, 76, 90

Offset: 0

Antti Karttunen, May 03 2017

The array is read by descending antidiagonals as A(0,0), A(0,1), A(1,0), A(0,2), A(1,1), A(2,0), ...

			The top left 0 .. 12 x 0 .. 12 corner of the array:
   0,   2,   5,   9,  14,  20,  27,  35,  44,  54,  65,  77,  90
   2,   1,  13,   8,  26,  19,  43,  34,  64,  53,  89,  76, 118
   5,  13,   3,   7,  42,  52,  25,  33,  88, 102,  63,  75, 150
   9,   8,   7,   6,  62,  51,  41,  32, 116, 101,  87,  74, 186
  14,  26,  42,  62,  10,  16,  23,  31, 148, 166, 185, 205,  86
  20,  19,  52,  51,  16,  15,  39,  30, 184, 165, 225, 204, 114
  27,  43,  25,  41,  23,  39,  21,  29, 224, 246, 183, 203, 146
  35,  34,  33,  32,  31,  30,  29,  28, 268, 245, 223, 202, 182
  44,  64,  88, 116, 148, 184, 224, 268,  36,  46,  57,  69,  82
  54,  53, 102, 101, 166, 165, 246, 245,  46,  45,  81,  68, 110
  65,  89,  63,  87, 185, 225, 183, 223,  57,  81,  55,  67, 142
  77,  76,  75,  74, 205, 204, 203, 202,  69,  68,  67,  66, 178
  90, 118, 150, 186,  86, 114, 146, 182,  82, 110, 142, 178,  78

Antti Karttunen, Table of n, a(n) for n = 0..10584; the first 145 antidiagonals of array
Eric Weisstein's World of Mathematics, Pairing Function

Cf. A000096 (row 0 & column 0), A000217 (main diagonal).

Cf. A003987, A001477, A286108, A286109, A286145, A286147, A286151.

T[a_, b_]:=((a + b)^2 + 3a + b)/2; A[n_, k_]:=T[BitXor[n, k],Min[n,  k]]; Table[A[k, n - k], {n, 0, 20}, {k, 0, n}] // Flatten (* Indranil Ghosh, May 21 2017 *)

def T(a, b): return ((a + b)**2 + 3*a + b)//2
def A(n, k): return T(n^k, min(n, k))
for n in range(21): print([A(k, n - k) for k in range(n + 1)]) # Indranil Ghosh, May 21 2017

(define (A286150 n) (A286150bi (A002262 n) (A025581 n)))
(define (A286150bi row col) (let ((a (A003987bi row col)) (b (min col row))) (/ (+ (expt (+ a b) 2) (* 3 a) b) 2))) ;; Where A003987bi implements bitwise-xor (A003987).

A(n,k) = T(A003987(n,k), min(n,k)), where T(n,k) is sequence A001477 considered as a two-dimensional table, that is, as a pairing function from [0, 1, 2, 3, ...] x [0, 1, 2, 3, ...] to [0, 1, 2, 3, ...].

A318507 a(n) = A032742(n) XOR A001065(n)-A032742(n), where XOR is bitwise-or (A003987) and A001065 = sum of proper divisors and A032742 = the largest proper divisor of n.

Original entry on oeis.org

1, 1, 1, 3, 1, 0, 1, 7, 2, 6, 1, 12, 1, 4, 1, 15, 1, 5, 1, 6, 3, 8, 1, 20, 4, 14, 13, 0, 1, 20, 1, 31, 15, 18, 1, 55, 1, 16, 9, 10, 1, 52, 1, 4, 29, 20, 1, 44, 6, 11, 21, 14, 1, 60, 13, 56, 23, 30, 1, 80, 1, 28, 1, 63, 11, 12, 1, 58, 19, 4, 1, 115, 1, 38, 1, 60, 3, 20, 1, 106, 22, 42, 1, 72, 23, 40, 25, 28, 1, 78, 5, 48, 27, 44, 21, 92, 1

Offset: 1

Antti Karttunen, Aug 28 2018

Note that here zeros occur only on even perfect numbers (even terms of A000396), in contrast to A318457, which would be zero also for any hypothetical odd perfect number. - Antti Karttunen, Aug 29 2018

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for sequences related to binary expansion of n

Cf. A000396, A001065, A003987, A032742, A318505, A318506, A318508.

Cf. also A106409, A318457, A318462, A318517.

A001065(n) = (sigma(n)-n);
A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));
A318505(n) = if(1==n,0,A001065(n)-A032742(n));
A318507(n) = bitxor(A318505(n),A032742(n));

a(n) = A003987(A032742(n), A318505(n)).

For n > 1, a(n) = A001065(n) - 2*A318508(n).

A318517 a(n) = A032742(n) XOR n-A032742(n), where XOR is bitwise-xor (A003987) and A032742 = the largest proper divisor of n.

Original entry on oeis.org

1, 0, 3, 0, 5, 0, 7, 0, 5, 0, 11, 0, 13, 0, 15, 0, 17, 0, 19, 0, 9, 0, 23, 0, 17, 0, 27, 0, 29, 0, 31, 0, 29, 0, 27, 0, 37, 0, 23, 0, 41, 0, 43, 0, 17, 0, 47, 0, 45, 0, 51, 0, 53, 0, 39, 0, 53, 0, 59, 0, 61, 0, 63, 0, 57, 0, 67, 0, 57, 0, 71, 0, 73, 0, 43, 0, 73, 0, 79, 0, 45, 0, 83, 0, 85, 0, 39, 0, 89, 0, 67, 0, 33, 0, 95

Offset: 1

Antti Karttunen, Aug 28 2018

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for sequences related to binary expansion of n

Cf. A003987, A032742, A060681, A106409, A318507, A318516, A318518.

A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));
A318517(n) = bitxor(A032742(n),n-A032742(n));

a(n) = A003987(A032742(n), A060681(n)).

a(n) = n - 2*A318518(n).

A324867 a(n) = A156552(n) XOR A324865(n), where XOR is bitwise-xor, A003987.

Original entry on oeis.org

0, 1, 3, 2, 7, 4, 15, 6, 0, 13, 31, 10, 63, 16, 2, 6, 127, 12, 255, 18, 7, 46, 511, 22, 28, 82, 4, 46, 1023, 30, 2047, 30, 54, 174, 2, 22, 4095, 256, 12, 54, 8191, 36, 16383, 66, 24, 798, 32767, 46, 60, 31, 248, 130, 65535, 28, 19, 70, 12, 1300, 131071, 42, 262143, 2734, 48, 22, 126, 94, 524287, 302, 774, 40, 1048575, 38, 2097151, 4354, 10

Offset: 1

Antti Karttunen, Mar 18 2019

nonn

Antti Karttunen, Table of n, a(n) for n = 1..10000 (based on Hans Havermann's factorization of A156552)
Index entries for sequences related to binary expansion of n
Index entries for sequences computed from indices in prime factorization
Index entries for sequences related to sigma(n)

Cf. A001065, A003986, A156552, A318457, A323243, A324865, A324866, A324398, A324877.

A156552(n) = {my(f = factor(n), p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552
A318457(n) = bitxor(n,sigma(n)-n);
A324867(n) = if(1==n,0,A318457(A156552(n)));

A324867(n) = { my(k=A156552(n)); bitxor(k,(A323243(n)-k)); }; \\ Needs also code from A323243.

a(1) = 0; for n > 1, a(n) = A318457(A156552(n)).
a(n) = A156552(n) XOR (A323243(n) - A156552(n)).
a(n) = A323243(n) - 2*A324398(n).

A372358 a(n) = n XOR A086893(1+A000523(n)), where XOR is a bitwise-XOR, A003987.

Original entry on oeis.org

0, 1, 0, 1, 0, 3, 2, 5, 4, 7, 6, 1, 0, 3, 2, 5, 4, 7, 6, 1, 0, 3, 2, 13, 12, 15, 14, 9, 8, 11, 10, 21, 20, 23, 22, 17, 16, 19, 18, 29, 28, 31, 30, 25, 24, 27, 26, 5, 4, 7, 6, 1, 0, 3, 2, 13, 12, 15, 14, 9, 8, 11, 10, 21, 20, 23, 22, 17, 16, 19, 18, 29, 28, 31, 30, 25, 24, 27, 26, 5, 4, 7, 6, 1, 0, 3, 2, 13, 12, 15

Offset: 1

Antti Karttunen, May 01 2024

a(n) gives n xored with the unique term of A086893 that has the same binary length as n itself. The binary expansions of the terms of A086893 are of the form 10101...0101 (i.e., alternating 1's and 0's starting and ending with 1) when the binary length is odd, and of the form 110101...0101 (i.e., 1 followed by alternating 1's and 0's, and ending with 1) when the binary length is even. In other words, a(n) is n with its all its even-positioned bits (indexing starts from 0 which stands for the least significant bit) inverted, and additionally also the odd-positioned most significant bit inverted if the number of significant bits is even (i.e., n is a nonzero term of A053754).

			25 in binary is 11001_2, and inverting all the even-positioned bits gives 01100_2, and as A007088(12) = 1100, a(25) = 12.
46 in binary is 101110_2, so we flip all the even-positioned bits (starting from the rightmost, with position 0), and because there are even number of bits in the binary expansion, we flip also the most significant bit, thus we obtain 011011_2, and as A007088(27) = 11011, a(46) = 27.

Antti Karttunen, Table of n, a(n) for n = 1..16384
Index entries for sequences related to binary expansion of n

Cf. A000523, A003987, A007088, A053754, A086893 (positions of 0's), A372359, A372360, A372361, A372446.

A000523(n) = logint(n,2);
A086893(n) = (if(n%2, 2^(n+1), 2^(n+1)+2^(n-1))\3); \\ From A086893
A372358(n) = bitxor(n, A086893(1+A000523(n)));

A283997 a(n) = n XOR A005187(floor(n/2)), where XOR is bitwise-xor (A003987).

Original entry on oeis.org

0, 1, 3, 2, 7, 6, 2, 3, 15, 14, 2, 3, 6, 7, 5, 4, 31, 30, 2, 3, 6, 7, 5, 4, 14, 15, 13, 12, 5, 4, 4, 5, 63, 62, 2, 3, 6, 7, 5, 4, 14, 15, 13, 12, 5, 4, 4, 5, 30, 31, 29, 28, 5, 4, 4, 5, 13, 12, 12, 13, 4, 5, 7, 6, 127, 126, 2, 3, 6, 7, 5, 4, 14, 15, 13, 12, 5, 4, 4, 5, 30, 31, 29, 28, 5, 4, 4, 5, 13, 12, 12, 13, 4, 5, 7, 6, 62, 63, 61, 60, 5, 4, 4, 5, 13, 12, 12

Offset: 0

Antti Karttunen, Mar 19 2017

Antti Karttunen, Table of n, a(n) for n = 0..8191
Index entries for sequences related to binary expansion of n

Cf. A003986, A005187, A006068, A283996, A283998, A283999.

Cf. also A279357, A283477.

Table[BitXor[n, 2 # - DigitCount[2 #, 2, 1] &@ Floor[n/2]], {n, 0, 106}] (* Michael De Vlieger, Mar 20 2017 *)

b(n) = if(n<1, 0, b(n\2) + n%2);
A(n) = 2*n - b(2*n);
for(n=0, 110, print1(bitxor(n, A(floor(n/2))),", ")) \\ Indranil Ghosh, Mar 25 2017

def A(n): return 2*n - bin(2*n)[2:].count("1")
print([n^A(n//2) for n in range(111)]) # Indranil Ghosh, Mar 25 2017

(define (A283997 n) (A003987bi n (A005187 (floor->exact (/ n 2))))) ;; Where A003987bi implements bitwise-XOR (A003987).

a(n) = n XOR A005187(floor(n/2)), where XOR is bitwise-xor (A003987).
a(n) = A283996(n) - A283998(n).
a(n) = A005187(n) - 2*A283998(n).
a(n) = A006068(n) XOR A283999(floor(n/2)).

A286153 Square array read by descending antidiagonals A(1,1), A(1,2), A(2,1), ...: If n > k, A(n,k) = T(n XOR k, k), and otherwise A(n,k) = T(n, n XOR k), where T(n,k) is sequence A001477 considered as a two-dimensional table, and XOR is bitwise-xor (A003987).

Original entry on oeis.org

2, 11, 13, 7, 5, 8, 22, 8, 7, 26, 16, 38, 9, 42, 19, 37, 47, 58, 62, 52, 43, 29, 23, 48, 14, 51, 25, 34, 56, 30, 39, 19, 16, 41, 33, 64, 46, 80, 31, 25, 20, 23, 32, 88, 53, 79, 93, 108, 32, 41, 39, 31, 116, 102, 89, 67, 57, 94, 140, 33, 27, 30, 148, 101, 63, 76, 106, 68, 81, 157, 176, 34, 29, 184, 166, 87, 75, 118, 92, 138, 69, 175, 158, 216, 35, 224, 165, 185, 74, 150, 103

Offset: 1

Antti Karttunen, May 03 2017

			The top left 1 .. 12 x 1 .. 12 corner of the array:
    2,  11,   7,  22,  16,  37,  29,  56,  46,  79,  67, 106
   13,   5,   8,  38,  47,  23,  30,  80,  93,  57,  68, 138
    8,   7,   9,  58,  48,  39,  31, 108,  94,  81,  69, 174
   26,  42,  62,  14,  19,  25,  32, 140, 157, 175, 194,  82
   19,  52,  51,  16,  20,  41,  33, 176, 158, 215, 195, 110
   43,  25,  41,  23,  39,  27,  34, 216, 237, 177, 196, 142
   34,  33,  32,  31,  30,  29,  35, 260, 238, 217, 197, 178
   64,  88, 116, 148, 184, 224, 268,  44,  53,  63,  74,  86
   53, 102, 101, 166, 165, 246, 245,  46,  54,  87,  75, 114
   89,  63,  87, 185, 225, 183, 223,  57,  81,  65,  76, 146
   76,  75,  74, 205, 204, 203, 202,  69,  68,  67,  77, 182
  118, 150, 186,  86, 114, 146, 182,  82, 110, 142, 178,  90

Antti Karttunen, Table of n, a(n) for n = 1..10585; the first 145 antidiagonals of array

Array A286151 without its topmost row and leftmost column.

Cf. A003987, A091255, A286155.

T[a_, b_]:=((a + b)^2 + 3a + b)/2; A[n_, k_]:=If[n>k,T[BitXor[n, k], k], T[n, BitXor[n, k]]]; Table[A[k, n - k + 1], {n, 20}, {k, n}] // Flatten (* Indranil Ghosh, May 21 2017 *)

def T(a, b): return ((a + b)**2 + 3*a + b)//2
def A(n, k): return T(n^k, k) if n>k else T(n, n^k)
for n in range(1, 21): print([A(k, n - k + 1) for k in range(1, n + 1)]) # Indranil Ghosh, May 21 2017

(define (A286153 n) (A286151bi (A002260 n) (A004736 n))) ;; For A286151bi see A286151.

A(n,k) = A286151(n,k), for n >= 1, k >= 1.

If n > k, A(n,k) = T(A003987(n,k),k), otherwise A(n,k) = T(n,A003987(n,k)), where T(n,k) is sequence A001477 considered as a two-dimensional table, and XOR is bitwise-xor (A003987).

A268726 Index of the toggled bit between n and A268717(n+1): a(n) = A000523(A003987(n, A268717(1+n))).

Original entry on oeis.org

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

Offset: 0

Antti Karttunen, Feb 13 2016

A fractal sequence, because a permutation of A007814. Removing zeros yields A268727(n) = a(n)+1.

Antti Karttunen, Table of n, a(n) for n = 0..16383
Indranil Ghosh, C program to generate the sequence

One less than A268727.
Cf. A003188, A006068.
Cf. A000523, A003987, A007814, A101080, A268717.
Cf. also array A268833.

A003188[n_]:=BitXor[n, Floor[n/2]]; A006068[n_]:=If[n<2, n, Block[{m=A006068[Floor[n/2]]}, 2m + Mod[Mod[n,2] + Mod[m, 2], 2]]]; A268717[n_]:=If[n<1, 0, A003188[1 + A006068[n - 1]]]; a[n_]:= Floor[Log[2, BitXor[n, A268717[n + 1]]]]; Table[a[n], {n, 0, 200}] (* Indranil Ghosh, Apr 02 2017 *)

A003188(n) = bitxor(n, n\2);
A006068(n) = if(n<2, n, {my(m = A006068(n\2)); 2*m + (n%2 + m%2)%2});
A268717(n) = if(n<1, 0, A003188(1 + A006068(n - 1)));
for(n=0, 200, print1(logint(bitxor(n, A268717(n + 1)), 2),", "))  \\ Indranil Ghosh, Apr 02 2017

def A003188(n): return n^(n//2)
def A006068(n):
    if n<2: return n
    else:
        m=A006068(n//2)
        return 2*m + (n%2 + m%2)%2
def A268717(n): return 0 if n<1 else A003188(1 + A006068(n - 1))
print([int(math.floor(math.log(n^A268717(n + 1), 2))) for n in range(201)]) # Indranil Ghosh, Apr 02 2017

(define (A268726 n) (A000523 (A003987bi n (A268717 (+ 1 n))))) ;; A003987bi implements the bitwise-XOR, defined in A003987.

a(n) = A007814(1 + A006068(n)).
a(n) = A000523(A003987(n, A268717(1+n))).
a(n) = floor(log_2(n XOR A003188(1 + A006068(n)))).
Other identities:
For all n >= 1, a(A003188(n-1)) = A007814(n).

A268727 One-based index of the toggled bit between n and A268717(n+1): a(n) = A070939(A003987(n,A268717(1+n))).

Original entry on oeis.org

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

Offset: 0

Antti Karttunen, Feb 13 2016

A fractal sequence like A268726.

Antti Karttunen, Table of n, a(n) for n = 0..8191

One more than A268726.
Cf. A003188, A006068.
Cf. A001511, A003987, A010059, A070939, A101080, A268717.
Cf. also array A268833.

(define (A268727 n) (A070939 (A003987bi n (A268717 (+ 1 n)))))  ;; A003987bi implements the bitwise-XOR, defined in A003987.

a(n) = A001511(1+A006068(n)).
a(n) = A070939(A003987(n,A268717(1+n))).
a(n) = 1 + floor(log_2(n XOR A003188(1+A006068(n)))).
a(n) = A001511(n)*(1-A010059(n)) + 1. - Alan Michael Gómez Calderón, Jun 15 2025

A283977 a(2n) = A002487(n), a(2n+1) = A002487(n) XOR A002487(n+1), where XOR is bitwise-xor (A003987).

Original entry on oeis.org

0, 1, 1, 0, 1, 3, 2, 3, 1, 2, 3, 1, 2, 1, 3, 2, 1, 5, 4, 7, 3, 6, 5, 7, 2, 7, 5, 6, 3, 7, 4, 5, 1, 4, 5, 1, 4, 3, 7, 4, 3, 11, 8, 13, 5, 2, 7, 5, 2, 5, 7, 2, 5, 13, 8, 11, 3, 4, 7, 3, 4, 1, 5, 4, 1, 7, 6, 3, 5, 12, 9, 13, 4, 15, 11, 12, 7, 13, 10, 9, 3, 8, 11, 3, 8, 5, 13, 8, 5, 9, 12, 11, 7, 14, 9, 11, 2, 11, 9, 14, 7, 11, 12, 9, 5, 8, 13, 5, 8, 3, 11, 8, 3

Offset: 0

Antti Karttunen, Mar 21 2017

Antti Karttunen, Table of n, a(n) for n = 0..8192
Index entries for sequences related to binary expansion of n

Bisections: A002487, A283987.

Cf. A003987, A283976, A283978.

a[0] = 0; a[1] = 1; a[n_] := If[EvenQ@ n, a[n/2], a[(n - 1)/2] + a[(n + 1)/2]]; Table[If[EvenQ@ n, a[n/2], BitXor[a[#], a[# + 1]] &[(n - 1)/2]], {n, 0, 112}] (* Michael De Vlieger, Mar 22 2017 *)

A(n) = if(n<2, n, if(n%2, A(n\2) + A((n + 1)/2), A(n/2)));
a(n) = if(n<2, n, if(n%2, bitxor(A(n\2), A((n + 1)/2)), A(n\2)));
for(n=0, 120, print1(a(n), ", ")) \\ Indranil Ghosh, Mar 23 2017

(define (A283977 n) (if (even? n) (A002487 n) (A003987bi (A002487 (/ (- n 1) 2)) (A002487 (/ (+ n 1) 2))))) ;; Where A003987bi implements bitwise-XOR (A003987).

a(2n) = A002487(2n) = A002487(n), a(2n+1) = A002487(n) XOR A002487(n+1), where XOR is bitwise-xor (A003987).
a(n) = A283976(n) - A283978(n).
a(n) = A002487(n) - 2*A283978(n).

cp's OEIS Frontend

A286150 Square array read by antidiagonals: A(n,k) = T(n XOR k, min(n,k)), where T(n,k) is sequence A001477 considered as a two-dimensional table, and XOR is bitwise-xor (A003987).

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A318507 a(n) = A032742(n) XOR A001065(n)-A032742(n), where XOR is bitwise-or (A003987) and A001065 = sum of proper divisors and A032742 = the largest proper divisor of n.

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A318517 a(n) = A032742(n) XOR n-A032742(n), where XOR is bitwise-xor (A003987) and A032742 = the largest proper divisor of n.

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PARI

Formula

A324867 a(n) = A156552(n) XOR A324865(n), where XOR is bitwise-xor, A003987.

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PARI

PARI

Formula

A372358 a(n) = n XOR A086893(1+A000523(n)), where XOR is a bitwise-XOR, A003987.

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PARI

A283997 a(n) = n XOR A005187(floor(n/2)), where XOR is bitwise-xor (A003987).

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Mathematica

PARI

Python

Scheme

Formula

A286153 Square array read by descending antidiagonals A(1,1), A(1,2), A(2,1), ...: If n > k, A(n,k) = T(n XOR k, k), and otherwise A(n,k) = T(n, n XOR k), where T(n,k) is sequence A001477 considered as a two-dimensional table, and XOR is bitwise-xor (A003987).

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Mathematica

Python

Scheme

Formula

A268726 Index of the toggled bit between n and A268717(n+1): a(n) = A000523(A003987(n, A268717(1+n))).

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