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A308306
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Boomerang numbers: their last digit "comes back" to occupy the place of their first digit (see the Comments section for the explanation).
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3
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100, 203, 225, 230, 247, 252, 269, 274, 296, 302, 320, 405, 427, 449, 450, 472, 494, 504, 522, 540, 607, 629, 670, 692, 706, 724, 742, 760, 809, 890, 908, 926, 944, 962, 980, 1012, 1021, 1034, 1043, 1056, 1065, 1078, 1087, 1102, 1120, 1201, 1210, 1223, 1232, 1245, 1254, 1267, 1276, 1289, 1298, 1304, 1322, 1340, 1403, 1425, 1430
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OFFSET
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1,1
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COMMENTS
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Take 2019; start with 2; jump over 2 cells to the right (as the even digits always move to the right); write 0 on the landing cell; jump over 0 cell to the right (which is the same as moving to the next cell to the right) and write 1 on the landing cell; as 1 is odd, jump over 1 cell to the left; write 9 on the landing cell; jump now over 9 cells to the left and mark A (for "Arrival") on the landing cell. The result will look like this (a dot is a cell): A.......2.901
As this A cell is not the same as the starting one (with "2"), 2019 is not a boomerang number. If we had taken 2011, we would have come back on the starting 2, like this:
2011
2..0
2..01
2.101
A.101
This is why 2011 is in the sequence and 2019 not.
Note that a cell, empty or not, is only a stopover: it can be used several times by different digits.
There are 263499 boomerang numbers < 10^7.
A boomerang number is easy to find, knowing the hereunder definition:
Integers B such that (the number of even digits + the sum of those) = (the number of odd digits + the sum of those).
Note: this sequence is not related to A256174 ("Boomerang fractions").
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LINKS
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EXAMPLE
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7308403 is a boomerang number as we have 4 even digits with sum 12 (4+12=16) and 3 odd digits with sum 13 (3+13=16).
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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STATUS
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approved
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