A365080 -id:A365080 - cp's OEIS frontend

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

Rémy Sigrist, Aug 12 2023

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.

			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
    ...

Rémy Sigrist, PARI program
Index entries for sequences that are permutations of the natural numbers

See A364884 for a similar sequence.

Cf. A000120, A057945, A365080 (inverse).

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

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

cp's OEIS Frontend

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.

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