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A275119
The even integers in the sequence appear in blocks and the successive sizes of these blocks are given by the sequence itself.
2
1, 2, 3, 4, 6, 5, 7, 8, 10, 12, 9, 11, 13, 14, 16, 18, 20, 15, 17, 19, 21, 22, 24, 26, 28, 30, 32, 23, 25, 27, 29, 31, 33, 34, 36, 38, 40, 42, 35, 37, 39, 41, 43, 44, 46, 48, 50, 52, 54, 56, 45, 47, 49, 51, 53, 55, 57, 58, 60, 62, 64, 66, 68, 70, 72, 59, 61, 63, 65, 67, 69, 71, 73, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93
OFFSET
1,2
COMMENTS
The sequence starts with a(1)=1 and is always extended with the smallest integer not yet in the sequence which does not lead to a contradiction. The sequence is a permutation of the natural numbers.
EXAMPLE
The blocks of even integers are indicated here by parentheses; the successive block-sizes are 1, 2, 3, 4, 6,... which reproduces the sequence itself: 1, (2), 3, (4, 6), 5, 7, (8, 10, 12), 9, 11, 13, (14, 16, 18, 20), 15, 17, 19, 21, (22, 24, 26, 28, 30, 32), 23, 25, 27, 29, 31, 33, (34, 36, 38, 40, 42), 35, 37, 39, 41, 43...
MATHEMATICA
s={1, 2, 3, 4, 6}; k=2; ev={4, 6}; Do[od=Range[ev[[1]]+1, ev[[-1]]+1, 2]; s=Flatten@{s, od}; a=od[[-1]]+1; k++; ev=Range[a, a+2*s[[k]]-2, 2]; s=Flatten@{s, ev}, {50}]; s
CROSSREFS
Sequence in context: A332807 A373038 A267106 * A218252 A080541 A330081
KEYWORD
nonn
AUTHOR
Zak Seidov and Eric Angelini, Jul 28 2016
STATUS
approved