A366626 Group the natural numbers into blocks of size 2: [1,2], [3,4], ... and then reverse the order of the numbers within each block. Then group and reverse for each block size up to 4.

5, 2, 1, 4, 7, 10, 3, 6, 9, 12, 11, 8, 17, 14, 13, 16, 19, 22, 15, 18, 21, 24, 23, 20, 29, 26, 25, 28, 31, 34, 27, 30, 33, 36, 35, 32, 41, 38, 37, 40, 43, 46, 39, 42, 45, 48, 47, 44, 53, 50, 49, 52, 55, 58, 51, 54, 57, 60, 59, 56, 65, 62, 61, 64, 67, 70, 63, 66, 69, 72, 71

Offset: 1

Author

Wesley Ivan Hurt, Oct 14 2023

Keywords

• nonn
• easy

Comments

Row 4 of the array in A007062.

Examples

			Group natural numbers into blocks of 2: [1, 2], [3, 4], [5, 6], [7, 8], ...
Reverse the order in each block: [2, 1], [4, 3], [6, 5], [8, 7], ...
Group the remaining sequence into blocks of 3: [2, 1, 4], [3, 6, 5], ...
Reverse the order in each block: [4, 1, 2], [5, 6, 3], ...
Group the remaining sequence into blocks of 4: [4, 1, 2, 5], [6, 3, 10, 7],
Reverse the order in each block to get a(n): 5, 2, 1, 4, 7, 10, 3, 6, ...
		

Links

• Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-2,2,-2,2,-2,2,-2,2,-1).

Crossrefs

Cf. A007062, A113778, A366619.

Programs

Mathematica

Table[1 + Mod[n + 1, 2] + 2 Floor[3 Floor[((1 + 4 Floor[(n - 1)/4] + Mod[-n, 4]) - 1)/3]/2 + Mod[-(1 + 4 Floor[(n - 1)/4] + Mod[-n, 4]), 3]/2], {n, 100}]

Formula

a(n) = A366619(A113778(n)).