A361674 Irregular triangle T(n, k), n >= 0, k = 1..2^A092339(n), read by rows; the n-th row lists the numbers k such that n appears in the k-th row of A361644.

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

Offset

0,3

Comments

In other words, the n-th row contains the numbers k with the same binary length as n and for any i >= 0, if the i-th bit and the (i+1)-th bit in n are different then they are also different in k (i = 0 corresponding to the least significant bit).

Links

Rémy Sigrist, Table of n, a(n) for n = 0..9841 (rows for n = 0..511 flattened)

Formula

T(n, 1) = A361645(n).

T(n, 2^A092339(n)) = A361676(n).

Example

Triangle T(n, k) begins (in decimal and in binary):
  n   n-th row        bin(n)  n-th row in binary
  --  --------------  ------  ----------------------
   0  0                    0  0
   1  1                    1  1
   2  2                   10  10
   3  2, 3                11  10, 11
   4  4, 5               100  100, 101
   5  5                  101  101
   6  5, 6               110  101, 110
   7  4, 5, 6, 7         111  100, 101, 110, 111
   8  8, 9, 10, 11      1000  1000, 1001, 1010, 1011
   9  9, 10             1001  1001, 1010
  10  10                1010  1010
  11  10, 11            1011  1010, 1011
  12  10, 11, 12, 13    1100  1010, 1011, 1100, 1101
  13  10, 13            1101  1010, 1101
  14  9, 10, 13, 14     1110  1001, 1010, 1101, 1110

Prog

(PARI) row(n) = { my (r = [n], m); for (e = 1, exponent(n), if (bittest(n, e-1)==bittest(n, e), m = 2^e-1; r = concat(r, [bitxor(v, m) | v <- r]); ); ); vecsort(r); }

Crossrefs

Cf. A361644, A361645, A361676.

Sequence in context: A069928 A135585 A081094 * A054633 A327982 A072490

Adjacent sequences: A361671 A361672 A361673 * A361675 A361676 A361677

Keyword

nonn,base,tabf

Author

Rémy Sigrist, Mar 20 2023

Status

approved