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A274500
The odd integers in the sequence appear in blocks and the successive sizes of these blocks are given by the sequence itself.
1
1, 2, 3, 5, 4, 6, 7, 9, 11, 8, 10, 12, 13, 15, 17, 19, 21, 14, 16, 18, 20, 22, 23, 25, 27, 29, 24, 26, 28, 30, 31, 33, 35, 37, 39, 41, 32, 34, 36, 38, 40, 42, 43, 45, 47, 49, 51, 53, 55, 44, 46, 48, 50, 52, 54, 56, 57, 59, 61, 63, 65, 67, 69, 71, 73, 58, 60, 62, 64, 66, 68, 70, 72, 74, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 76, 78, 80, 82, 84, 86, 88, 90
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 odd integers are indicated here by parentheses; the successive block-sizes are1,2,3,5,4,6,7,9,11,8,10,... which reproduces the sequence itself:
(1),2,(3,5),4,6,(7,9,11),8,10,12,(13,15,17,19,21),14,16,18,20,22,(23,25,27,29),24,26,28,30,(31,33,35,37,39,41),
32,34,36,38,40,42,(43,45,47,49,51,53,55),44,46,48,50,52,54,56,(57,59,61,63,65,67,69,71,73),58,60,62,64,66,68,70,72,74,
(75,77,79,81,83,85,87,89,91,93,95),76,78,80,82,84,86,88,90,92,94,96,(97,99,101,103,105,107,109,111),
98,100,102,104,106,108,110,112,(113,115,117,119,121,123,125,127,129,131),...
MATHEMATICA
s={1, 2, 3, 5}; k=2; od={3, 5}; Do[ev=Range[od[[1]]+1, od[[-1]]+1, 2]; s=Flatten@{s, ev}; a=ev[[-1]]+1; k++; od=Range[a, a+2*s[[k]]-2, 2]; s=Flatten@{s, od}, {100}]; s
CROSSREFS
Sequence in context: A225047 A279338 A279348 * A123917 A344682 A344962
KEYWORD
nonn,base
AUTHOR
Zak Seidov and Eric Angelini, Jul 28 2016
STATUS
approved