A161373 "Early bird" binary numbers: write the natural numbers in binary representation in a string 011011100101110111.... Sequence gives numbers which occur in the string strictly ahead of their natural place.
3, 5, 6, 7, 9, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65
Offset: 1
Examples
Decimal 0 1 2 3 4 5 ... Binary 0 1 10 11 100 101 ... 3 is before its natural position ('1' + beginning of '2' -> 011...) The same for : 5: '2' + beginning of '3' -> 01101... 6: '1' + '2' -> 0110... etc. In the first 5 binary numbers we can find ahead of their natural place: 3,5,6,7,9,11,12,13,14,18,23,25,27,28,37,46,50,55,57
20 ('10100') occurs at the joint of 18 and 19: the last 2 digits of '10010' and the first three of '10011'
Links
- H. v. Eitzen, Binary Early Birds (2009).
Extensions
"Strictly" added to definition, offset corrected as customary for lists, 20 added by Hagen von Eitzen, Jun 27 2009
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