A360364 Triangle T(n, k), n > 0, k = 1..n, read by rows; T(n, k) = A360363(n+1) XOR A360363(k) (where XOR denotes the bitwise XOR operator).

3, 2, 1, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 8, 4, 17, 18, 19, 20, 24, 28, 33, 34, 35, 36, 40, 44, 48, 49, 50, 51, 52, 56, 60, 32, 16, 65, 66, 67, 68, 72, 76, 80, 96, 112, 84, 87, 86, 81, 93, 89, 69, 117, 101, 21, 107, 104, 105, 110, 98, 102, 122, 74, 90, 42, 63

Offset

1,1

Comments

All terms are distinct.

Every positive integer appears in this sequence:

- each time a power of 2 appears in A360363, say A360363(n) = 2^k,

- if the least value v missing from the bitwise XOR of two distinct terms among the first n terms of A360363 satisfies v < 2^k,

- then A360363(n+1) = 2^k + v and T(n,n) = v.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..7021

Rémy Sigrist, Scatterplot of (n, T(n, k)) for n = 1..1227, k = 1..n

Rémy Sigrist, Colored representation of the first 1227 rows (where the hue is function of T(n, k))

Rémy Sigrist, C++ program

Index entries for sequences that are permutations of the natural numbers

Example

Table begins:
    3,
    2, 1,
    5, 6, 7,
    9, 10, 11, 12,
    13, 14, 15, 8, 4,
    17, 18, 19, 20, 24, 28,
    33, 34, 35, 36, 40, 44, 48,
    49, 50, 51, 52, 56, 60, 32, 16,
    65, 66, 67, 68, 72, 76, 80, 96, 112,
    84, 87, 86, 81, 93, 89, 69, 117, 101, 21,
    107, 104, 105, 110, 98, 102, 122, 74, 90, 42, 63,
    129, 130, 131, 132, 136, 140, 144, 160, 176, 192, 213, 234,
    151, 148, 149, 146, 158, 154, 134, 182, 166, 214, 195, 252, 22,
    ...

Prog

(C++) See Links section.

Crossrefs

Cf. A360363.

Sequence in context: A138483 A110712 A065366 * A092879 A073370 A208511

Adjacent sequences: A360361 A360362 A360363 * A360365 A360366 A360367

Keyword

nonn,base,look,tabl

Author

Rémy Sigrist, Feb 04 2023

Status

approved