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

1,1

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

Links

Table of n, a(n) for n=1..55.

H. v. Eitzen, Binary Early Birds (2009).

Example

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'

Crossrefs

Cf. A116700, A161374, A296365.

Sequence in context: A296365 A291166 A333228 * A333227 A285510 A174415

Adjacent sequences: A161370 A161371 A161372 * A161374 A161375 A161376

Keyword

easy,nonn

Author

Paolo P. Lava and Giorgio Balzarotti, Jun 08 2009

Extensions

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

Status

approved