A070939 -id:A070939 - cp's OEIS frontend

A334594 Irregular table read by rows: T(n,k) is the binary interpretation of the k-th row of the XOR-triangle with first row generated from the binary expansion of n. 1 <= k <= A070939(n).

1, 2, 1, 3, 0, 4, 2, 1, 5, 3, 0, 6, 1, 1, 7, 0, 0, 8, 4, 2, 1, 9, 5, 3, 0, 10, 7, 0, 0, 11, 6, 1, 1, 12, 2, 3, 0, 13, 3, 2, 1, 14, 1, 1, 1, 15, 0, 0, 0, 16, 8, 4, 2, 1, 17, 9, 5, 3, 0, 18, 11, 6, 1, 1, 19, 10, 7, 0, 0, 20, 14, 1, 1, 1, 21, 15, 0, 0, 0

Offset: 1

Peter Kagey, May 07 2020

An XOR-triangle is an inverted 0-1 triangle formed by choosing a top row and having each entry in the subsequent rows be the XOR of the two values above it.

The second column is A038554.

			Table begins:
   1;
   2, 1;
   3, 0;
   4, 2, 1;
   5, 3, 0;
   6, 1, 1;
   7, 0, 0;
   8, 4, 2, 1;
   9, 5, 3, 0;
  10, 7, 0, 0;
  11, 6, 1, 1;
For the 11th row, the binary expansion of 11 is 1011_2, and the corresponding XOR-triangle is
  1 0 1 1
   1 1 0
    0 1
     1
Reading the rows of this triangle in binary gives 11, 6, 1, 1.

Peter Kagey, Table of n, a(n) for n = 1..9217 (first 1023 rows)
MathOverflow user DSM, Number triangle
Index entries for sequences related to binary expansion of n

Cf. A038554, A070939.

Cf. A334556, A334591, A334592, A334593, A334595, A334596.

Array[Prepend[FromDigits[#, 2] & /@ #2, #1] & @@ {#, Rest@ NestWhileList[Map[BitXor @@ # &, Partition[#, 2, 1]] &, IntegerDigits[#, 2], Length@ # > 1 &]} &, 21] // Flatten (* Michael De Vlieger, May 08 2020 *)

row(n) = {my(b=binary(n), v=vector(#b)); v[1] = n; for (n=1, #b-1, b = vector(#b-1, k, bitxor(b[k], b[k+1])); v[n+1] = fromdigits(b, 2);); v;} \\ Michel Marcus, May 08 2020

A030530 n appears A070939(n) times.

Original entry on oeis.org

0, 1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 20, 20, 20, 20, 20, 21, 21, 21

Offset: 0

J. Lowell

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Cf. A030190, A053738, A070939, A083651, A083652.

import Data.List (unfoldr)
a030530 n = a030530_list !! (n-1)
a030530_list = 0 : concatMap (\n -> unfoldr
   (\x -> if x == 0 then Nothing else Just (n, div x 2)) n) [1..]
-- Reinhard Zumkeller, Dec 05 2011

Join[{0},Table[Table[n,IntegerLength[n,2]],{n,30}]]//Flatten (* Harvey P. Dale, Oct 20 2016 *)

A030190(n) = T(a(n), A083652(a(n))-n-1), T as defined in A083651.
a(A083652(k)) = k+1.
Sum_{n>=1} (-1)^(n+1)/a(n) = Sum_{n>=1} (-1)^(n+1)/A053738(n) = 0.90457767... . - Amiram Eldar, Feb 18 2024

A214489 Numbers m such that A070939(m) = A070939(m + A070939(m)), A070939 = length of binary representation.

Original entry on oeis.org

0, 4, 8, 9, 10, 11, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86

Offset: 1

Reinhard Zumkeller, Jul 21 2012

nonn

A070939(a(n))=A103586(a(n)) and also A105025(a(n))=A105029(a(n)).

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers [pdf, ps].
Index entries for sequences related to binary expansion of n

a214489 n = a214489_list !! (n-1)
a214489_list = [x | x <- [0..], a070939 x == a103586 x]
-- .

A344834 Square array T(n, k), n, k >= 0, read by antidiagonals; T(n, k) = (n * 2^max(0, w(k)-w(n))) AND (k * 2^max(0, w(n)-w(k))) (where AND denotes the bitwise AND operator and w = A070939).

Original entry on oeis.org

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

Offset: 0

Rémy Sigrist, May 29 2021

In other words, we right pad the binary expansion of the lesser of n and k with zeros (provided it is positive) so that both numbers have the same number of binary digits, and then apply the bitwise AND operator.

			Array T(n, k) begins:
  n\k|  0  1  2   3  4   5   6   7  8  9  10  11  12  13  14  15
  ---+----------------------------------------------------------
    0|  0  0  0   0  0   0   0   0  0  0   0   0   0   0   0   0
    1|  0  1  2   2  4   4   4   4  8  8   8   8   8   8   8   8
    2|  0  2  2   2  4   4   4   4  8  8   8   8   8   8   8   8
    3|  0  2  2   3  4   4   6   6  8  8   8   8  12  12  12  12
    4|  0  4  4   4  4   4   4   4  8  8   8   8   8   8   8   8
    5|  0  4  4   4  4   5   4   5  8  8  10  10   8   8  10  10
    6|  0  4  4   6  4   4   6   6  8  8   8   8  12  12  12  12
    7|  0  4  4   6  4   5   6   7  8  8  10  10  12  12  14  14
    8|  0  8  8   8  8   8   8   8  8  8   8   8   8   8   8   8
    9|  0  8  8   8  8   8   8   8  8  9   8   9   8   9   8   9
   10|  0  8  8   8  8  10   8  10  8  8  10  10   8   8  10  10
   11|  0  8  8   8  8  10   8  10  8  9  10  11   8   9  10  11
   12|  0  8  8  12  8   8  12  12  8  8   8   8  12  12  12  12
   13|  0  8  8  12  8   8  12  12  8  9   8   9  12  13  12  13
   14|  0  8  8  12  8  10  12  14  8  8  10  10  12  12  14  14
   15|  0  8  8  12  8  10  12  14  8  9  10  11  12  13  14  15

Rémy Sigrist, Table of n, a(n) for n = 0..10010
Rémy Sigrist, Colored representation of the table for n, k < 2^10

Cf. A004198, A053644, A070939.

Cf. A344835 (OR), A344836 (XOR), A344837 (min), A344838 (max), A344839 (absolute difference).

T(n,k,op=bitand,w=m->#binary(m)) = { op(n*2^max(0, w(k)-w(n)), k*2^max(0, w(n)-w(k))) }

T(n, k) = T(k, n).
T(m, T(n, k)) = T(T(m, n), k).
T(n, n) = n.
T(n, 0) = n.
T(n, 1) = A053644(n).

A344835 Square array T(n, k), n, k >= 0, read by antidiagonals; T(n, k) = (n * 2^max(0, w(k)-w(n))) OR (k * 2^max(0, w(n)-w(k))) (where OR denotes the bitwise OR operator and w = A070939).

Original entry on oeis.org

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

Offset: 0

Rémy Sigrist, May 29 2021

In other words, we right pad the binary expansion of the lesser of n and k with zeros (provided it is positive) so that both numbers have the same number of binary digits, and then apply the bitwise OR operator.

			Array T(n, k) begins:
  n\k|   0   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15
  ---+----------------------------------------------------------------
    0|   0   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15
    1|   1   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15
    2|   2   2   2   3   4   5   6   7   8   9  10  11  12  13  14  15
    3|   3   3   3   3   6   7   6   7  12  13  14  15  12  13  14  15
    4|   4   4   4   6   4   5   6   7   8   9  10  11  12  13  14  15
    5|   5   5   5   7   5   5   7   7  10  11  10  11  14  15  14  15
    6|   6   6   6   6   6   7   6   7  12  13  14  15  12  13  14  15
    7|   7   7   7   7   7   7   7   7  14  15  14  15  14  15  14  15
    8|   8   8   8  12   8  10  12  14   8   9  10  11  12  13  14  15
    9|   9   9   9  13   9  11  13  15   9   9  11  11  13  13  15  15
   10|  10  10  10  14  10  10  14  14  10  11  10  11  14  15  14  15
   11|  11  11  11  15  11  11  15  15  11  11  11  11  15  15  15  15
   12|  12  12  12  12  12  14  12  14  12  13  14  15  12  13  14  15
   13|  13  13  13  13  13  15  13  15  13  13  15  15  13  13  15  15
   14|  14  14  14  14  14  14  14  14  14  15  14  15  14  15  14  15
   15|  15  15  15  15  15  15  15  15  15  15  15  15  15  15  15  15

Rémy Sigrist, Table of n, a(n) for n = 0..10010
Rémy Sigrist, Colored representation of the table for n, k < 2^10

Cf. A003986, A070939.

Cf. A344834 (AND), A344836 (XOR), A344837 (min), A344838 (max), A344839 (absolute difference).

T(n, k, op=bitor, w=m->#binary(m)) = { op(n*2^max(0, w(k)-w(n)), k*2^max(0, w(n)-w(k))) }

T(n, k) = T(k, n).
T(m, T(n, k)) = T(T(m, n), k).
T(n, n) = n.
T(n, 0) = n.
T(n, 1) = max(1, n).

A344836 Square array T(n, k), n, k >= 0, read by antidiagonals; T(n, k) = (n * 2^max(0, w(k)-w(n))) XOR (k * 2^max(0, w(n)-w(k))) (where XOR denotes the bitwise XOR operator and w = A070939).

Original entry on oeis.org

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

Offset: 0

Rémy Sigrist, May 29 2021

In other words, we right pad the binary expansion of the lesser of n and k with zeros (provided it is positive) so that both numbers have the same number of binary digits, and then apply the bitwise XOR operator.

			Array T(n, k) begins:
  n\k|   0  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15
  ---+-------------------------------------------------------
    0|   0  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15
    1|   1  0  0  1  0  1  2  3  0  1   2   3   4   5   6   7
    2|   2  0  0  1  0  1  2  3  0  1   2   3   4   5   6   7
    3|   3  1  1  0  2  3  0  1  4  5   6   7   0   1   2   3
    4|   4  0  0  2  0  1  2  3  0  1   2   3   4   5   6   7
    5|   5  1  1  3  1  0  3  2  2  3   0   1   6   7   4   5
    6|   6  2  2  0  2  3  0  1  4  5   6   7   0   1   2   3
    7|   7  3  3  1  3  2  1  0  6  7   4   5   2   3   0   1
    8|   8  0  0  4  0  2  4  6  0  1   2   3   4   5   6   7
    9|   9  1  1  5  1  3  5  7  1  0   3   2   5   4   7   6
   10|  10  2  2  6  2  0  6  4  2  3   0   1   6   7   4   5
   11|  11  3  3  7  3  1  7  5  3  2   1   0   7   6   5   4
   12|  12  4  4  0  4  6  0  2  4  5   6   7   0   1   2   3
   13|  13  5  5  1  5  7  1  3  5  4   7   6   1   0   3   2
   14|  14  6  6  2  6  4  2  0  6  7   4   5   2   3   0   1
   15|  15  7  7  3  7  5  3  1  7  6   5   4   3   2   1   0

Rémy Sigrist, Table of n, a(n) for n = 0..10010
Rémy Sigrist, Colored representation of the table for n, k < 2^10

Cf. A003987, A053645, A070939.

Cf. A344834 (AND), A344835 (OR), A344837 (min), A344838 (max), A344839 (absolute difference).

T(n, k, op=bitxor, w=m->#binary(m)) = { op(n*2^max(0, w(k)-w(n)), k*2^max(0, w(n)-w(k))) }

T(n, k) = T(k, n).
T(n, n) = 0.
T(n, 0) = n.
T(n, 1) = A053645(n) for any n > 0.

A344837 Square array T(n, k), n, k >= 0, read by antidiagonals; T(n, k) = min(n * 2^max(0, w(k)-w(n)), k * 2^max(0, w(n)-w(k))) (where w = A070939).

Original entry on oeis.org

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

Offset: 0

Rémy Sigrist, May 29 2021

In other words, we right pad the binary expansion of the lesser of n and k with zeros (provided it is positive) so that both numbers have the same number of binary digits, and then take the least value.

			Array T(n, k) begins:
  n\k|  0  1  2   3  4   5   6   7  8  9  10  11  12  13  14  15
  ---+----------------------------------------------------------
    0|  0  0  0   0  0   0   0   0  0  0   0   0   0   0   0   0
    1|  0  1  2   2  4   4   4   4  8  8   8   8   8   8   8   8
    2|  0  2  2   2  4   4   4   4  8  8   8   8   8   8   8   8
    3|  0  2  2   3  4   5   6   6  8  9  10  11  12  12  12  12
    4|  0  4  4   4  4   4   4   4  8  8   8   8   8   8   8   8
    5|  0  4  4   5  4   5   5   5  8  9  10  10  10  10  10  10
    6|  0  4  4   6  4   5   6   6  8  9  10  11  12  12  12  12
    7|  0  4  4   6  4   5   6   7  8  9  10  11  12  13  14  14
    8|  0  8  8   8  8   8   8   8  8  8   8   8   8   8   8   8
    9|  0  8  8   9  8   9   9   9  8  9   9   9   9   9   9   9
   10|  0  8  8  10  8  10  10  10  8  9  10  10  10  10  10  10
   11|  0  8  8  11  8  10  11  11  8  9  10  11  11  11  11  11
   12|  0  8  8  12  8  10  12  12  8  9  10  11  12  12  12  12
   13|  0  8  8  12  8  10  12  13  8  9  10  11  12  13  13  13
   14|  0  8  8  12  8  10  12  14  8  9  10  11  12  13  14  14
   15|  0  8  8  12  8  10  12  14  8  9  10  11  12  13  14  15

Rémy Sigrist, Table of n, a(n) for n = 0..10010
Rémy Sigrist, Colored representation of the table for n, k < 2^10

Cf. A003983, A053644, A070939.

Cf. A344834 (AND), A344835 (OR), A344836 (XOR), A344838 (max), A344839 (absolute difference).

T(n, k, op=min, w=m->#binary(m)) = { op(n*2^max(0, w(k)-w(n)), k*2^max(0, w(n)-w(k))) }

T(n, k) = T(k, n).
T(m, T(n, k)) = T(T(m, n), k).
T(n, n) = n.
T(n, 0) = 0.
T(n, 1) = A053644(n).

A344838 Square array T(n, k), n, k >= 0, read by antidiagonals; T(n, k) = max(n * 2^max(0, w(k)-w(n)), k * 2^max(0, w(n)-w(k))) (where w = A070939).

Original entry on oeis.org

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

Offset: 0

Rémy Sigrist, May 29 2021

In other words, we right pad the binary expansion of the lesser of n and k with zeros (provided it is positive) so that both numbers have the same number of binary digits, and then take the greatest value.

			Array T(n, k) begins:
  n\k|   0   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15
  ---+----------------------------------------------------------------
    0|   0   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15
    1|   1   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15
    2|   2   2   2   3   4   5   6   7   8   9  10  11  12  13  14  15
    3|   3   3   3   3   6   6   6   7  12  12  12  12  12  13  14  15
    4|   4   4   4   6   4   5   6   7   8   9  10  11  12  13  14  15
    5|   5   5   5   6   5   5   6   7  10  10  10  11  12  13  14  15
    6|   6   6   6   6   6   6   6   7  12  12  12  12  12  13  14  15
    7|   7   7   7   7   7   7   7   7  14  14  14  14  14  14  14  15
    8|   8   8   8  12   8  10  12  14   8   9  10  11  12  13  14  15
    9|   9   9   9  12   9  10  12  14   9   9  10  11  12  13  14  15
   10|  10  10  10  12  10  10  12  14  10  10  10  11  12  13  14  15
   11|  11  11  11  12  11  11  12  14  11  11  11  11  12  13  14  15
   12|  12  12  12  12  12  12  12  14  12  12  12  12  12  13  14  15
   13|  13  13  13  13  13  13  13  14  13  13  13  13  13  13  14  15
   14|  14  14  14  14  14  14  14  14  14  14  14  14  14  14  14  15
   15|  15  15  15  15  15  15  15  15  15  15  15  15  15  15  15  15

Rémy Sigrist, Table of n, a(n) for n = 0..10010
Rémy Sigrist, Colored representation of the table for n, k < 2^10

Cf. A003984, A070939.

Cf. A344834 (AND), A344835 (OR), A344836 (XOR), A344837 (min), A344839 (absolute difference).

T(n,k,op=max,w=m->#binary(m)) = { op(n*2^max(0, w(k)-w(n)), k*2^max(0, w(n)-w(k))) }

T(n, k) = T(k, n).
T(m, T(n, k)) = T(T(m, n), k).
T(n, n) = n.
T(n, 0) = n.
T(n, 1) = max(1, n).

A344839 Square array T(n, k), n, k >= 0, read by antidiagonals; T(n, k) = abs(n * 2^max(0, w(k)-w(n)) - k * 2^max(0, w(n)-w(k))) (where w = A070939).

Original entry on oeis.org

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

Offset: 0

Rémy Sigrist, May 29 2021

In other words, we right pad the binary expansion of the lesser of n and k with zeros (provided it is positive) so that both numbers have the same number of binary digits, and then take the absolute difference.

			Array T(n, k) begins:
  n\k|   0  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15
  ---+-------------------------------------------------------
    0|   0  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15
    1|   1  0  0  1  0  1  2  3  0  1   2   3   4   5   6   7
    2|   2  0  0  1  0  1  2  3  0  1   2   3   4   5   6   7
    3|   3  1  1  0  2  1  0  1  4  3   2   1   0   1   2   3
    4|   4  0  0  2  0  1  2  3  0  1   2   3   4   5   6   7
    5|   5  1  1  1  1  0  1  2  2  1   0   1   2   3   4   5
    6|   6  2  2  0  2  1  0  1  4  3   2   1   0   1   2   3
    7|   7  3  3  1  3  2  1  0  6  5   4   3   2   1   0   1
    8|   8  0  0  4  0  2  4  6  0  1   2   3   4   5   6   7
    9|   9  1  1  3  1  1  3  5  1  0   1   2   3   4   5   6
   10|  10  2  2  2  2  0  2  4  2  1   0   1   2   3   4   5
   11|  11  3  3  1  3  1  1  3  3  2   1   0   1   2   3   4
   12|  12  4  4  0  4  2  0  2  4  3   2   1   0   1   2   3
   13|  13  5  5  1  5  3  1  1  5  4   3   2   1   0   1   2
   14|  14  6  6  2  6  4  2  0  6  5   4   3   2   1   0   1
   15|  15  7  7  3  7  5  3  1  7  6   5   4   3   2   1   0

Rémy Sigrist, Table of n, a(n) for n = 0..10010
Rémy Sigrist, Colored representation of the table for n, k < 2^10

Cf. A049581, A053645, A070939.

Cf. A344834 (AND), A344835 (OR), A344836 (XOR), A344837 (min), A344838 (max).

T(n,k,op=(x,y)->abs(x-y),w=m->#binary(m)) = { op(n*2^max(0, w(k)-w(n)), k*2^max(0, w(n)-w(k))) }

T(n, k) = T(k, n).
T(n, n) = 0.
T(n, 0) = n.
T(n, 1) = A053645(n) for any n > 0.

A266197 Indices of "good matches" produced by match-making permutation A266195; numbers n for which A070939(A266195(n)) = A070939(A266195(n+1)), where A070939(n) gives the length of base-2 representation of n.

Original entry on oeis.org

2, 4, 5, 9, 10, 18, 19, 26, 34, 37, 38, 58, 61, 62, 66, 67, 129, 130, 133, 137, 138, 158, 286, 287, 290, 292, 301, 302, 311, 318, 365, 366, 371, 379, 382, 384, 561, 562, 563, 627, 628, 629, 630, 631, 633, 639, 644, 646, 680, 683, 688, 767, 768, 775, 776, 777, 778, 780, 913, 914, 915, 918, 919, 920, 923, 924, 925, 926, 927, 928, 930, 931, 932, 933, 939, 1315

Offset: 1

Antti Karttunen, Dec 26 2015

Numbers n for which A264982(n) = A264982(n+1).

It would be nice to know whether this sequence is infinite.

Rémy Sigrist, Table of n, a(n) for n = 1..10000 (first 154 terms from Antti Karttunen)

Cf. A070939, A264982, A266195.

Cf. A265748, A265749 (give the first and second members of pairs indexed by this sequence).

cp's OEIS Frontend

A334594 Irregular table read by rows: T(n,k) is the binary interpretation of the k-th row of the XOR-triangle with first row generated from the binary expansion of n. 1 <= k <= A070939(n).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

A030530 n appears A070939(n) times.

Views

Author

Keywords

Links

Crossrefs

Programs

Haskell

Mathematica

Formula

A214489 Numbers m such that A070939(m) = A070939(m + A070939(m)), A070939 = length of binary representation.

Views

Author

Keywords

Comments

Links

Programs

Haskell

A344834 Square array T(n, k), n, k >= 0, read by antidiagonals; T(n, k) = (n * 2^max(0, w(k)-w(n))) AND (k * 2^max(0, w(n)-w(k))) (where AND denotes the bitwise AND operator and w = A070939).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

Formula

A344835 Square array T(n, k), n, k >= 0, read by antidiagonals; T(n, k) = (n * 2^max(0, w(k)-w(n))) OR (k * 2^max(0, w(n)-w(k))) (where OR denotes the bitwise OR operator and w = A070939).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

Formula

A344836 Square array T(n, k), n, k >= 0, read by antidiagonals; T(n, k) = (n * 2^max(0, w(k)-w(n))) XOR (k * 2^max(0, w(n)-w(k))) (where XOR denotes the bitwise XOR operator and w = A070939).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

Formula

A344837 Square array T(n, k), n, k >= 0, read by antidiagonals; T(n, k) = min(n * 2^max(0, w(k)-w(n)), k * 2^max(0, w(n)-w(k))) (where w = A070939).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

Formula

A344838 Square array T(n, k), n, k >= 0, read by antidiagonals; T(n, k) = max(n * 2^max(0, w(k)-w(n)), k * 2^max(0, w(n)-w(k))) (where w = A070939).

Views

Author

Keywords

Comments

Examples