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

Author

Paolo P. Lava and Giorgio Balzarotti, Jun 08 2009

Keywords

• easy
• nonn

Comments

A161373 U A161374 = A000027.

In contrast to sequences A048991, A048992 (Hannah Rollman's numbers), and binary analogs A190784 and related, the numbers listed here are repeated in their natural position when forming the concatenation of binary digits, even though they occur already earlier in the string. - M. F. Hasler, Jan 01 2013

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).

Crossrefs

Cf. A116700, A161374, A296365.

Extensions

"Strictly" added to definition, offset corrected as customary for lists, 20 added by Hagen von Eitzen, Jun 27 2009