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

Author

Rémy Sigrist, Feb 04 2023

Keywords

• nonn
• base
• look
• tabl

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.

Examples

			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,
    ...
		

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

Crossrefs

Cf. A360363.