A364885 Triangle T(n, k), n >= 0, k = 0..n, read by rows; T(0, 0) = 0, and for any n > 0, k = 0..n, T(n, k) is the least number obtained by turning a 0 into a 1 in the binary expansion of the k-th term of the (0-based) flattened sequence.

0, 1, 3, 2, 5, 7, 4, 9, 11, 6, 8, 17, 19, 10, 13, 16, 33, 35, 18, 21, 15, 32, 65, 67, 34, 37, 23, 12, 64, 129, 131, 66, 69, 39, 20, 25, 128, 257, 259, 130, 133, 71, 36, 41, 27, 256, 513, 515, 258, 261, 135, 68, 73, 43, 14, 512, 1025, 1027, 514, 517, 263, 132, 137, 75, 22, 24

Offset

0,3

Comments

In other words, T(n, k) = a(k) OR 2^e for some e >= 0 (where OR denotes the bitwise OR operator).

As a flat sequence, this is a permutation of the nonnegative integers (as, for any h >= 0, the sequence contains all numbers with Hamming weight h); see A365080 for the inverse.

Links

Table of n, a(n) for n=0..65.

Rémy Sigrist, PARI program

Index entries for sequences that are permutations of the natural numbers

Formula

T(n, 0) = 2^(n-1) for any n > 0.

A000120(a(n)) = A057945(n).

Example

Triangle begins:
    0
    1, 3
    2, 5, 7
    4, 9, 11, 6
    8, 17, 19, 10, 13
    16, 33, 35, 18, 21, 15
    32, 65, 67, 34, 37, 23, 12
    64, 129, 131, 66, 69, 39, 20, 25
    128, 257, 259, 130, 133, 71, 36, 41, 27
    256, 513, 515, 258, 261, 135, 68, 73, 43, 14
    512, 1025, 1027, 514, 517, 263, 132, 137, 75, 22, 24
    ...

Prog

(PARI) See Links section.

Crossrefs

See A364884 for a similar sequence.

Cf. A000120, A057945, A365080 (inverse).

Sequence in context: A209140 A265903 A345420 * A006369 A097284 A276684

Adjacent sequences: A364882 A364883 A364884 * A364886 A364887 A364888

Keyword

nonn,base,tabl

Author

Rémy Sigrist, Aug 12 2023

Status

approved