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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.
0
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
1,1
COMMENTS
Row 4 of the array in A007062.
FORMULA
a(n) = A366619(A113778(n)).
EXAMPLE
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, ...
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}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Oct 14 2023
STATUS
approved