A364885 - OEIS

%I #9 Aug 26 2023 08:57:09

%S 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,

%T 23,12,64,129,131,66,69,39,20,25,128,257,259,130,133,71,36,41,27,256,

%U 513,515,258,261,135,68,73,43,14,512,1025,1027,514,517,263,132,137,75,22,24

%N 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.

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

%C 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.

%H Rémy Sigrist, <a href="/A364885/a364885.gp.txt">PARI program</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

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

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

%e Triangle begins:

%e     0

%e     1, 3

%e     2, 5, 7

%e     4, 9, 11, 6

%e     8, 17, 19, 10, 13

%e     16, 33, 35, 18, 21, 15

%e     32, 65, 67, 34, 37, 23, 12

%e     64, 129, 131, 66, 69, 39, 20, 25

%e     128, 257, 259, 130, 133, 71, 36, 41, 27

%e     256, 513, 515, 258, 261, 135, 68, 73, 43, 14

%e     512, 1025, 1027, 514, 517, 263, 132, 137, 75, 22, 24

%e     ...

%o (PARI) See Links section.

%Y See A364884 for a similar sequence.

%Y Cf. A000120, A057945, A365080 (inverse).

%K nonn,base,tabl

%O 0,3

%A _Rémy Sigrist_, Aug 12 2023