A364885 - OEIS

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

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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:

1, 3

2, 5, 7

4, 9, 11, 6