cp's OEIS Frontend

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.

%I A161373 #14 Dec 14 2022 12:35:05
%S A161373 3,5,6,7,9,11,12,13,14,15,17,18,19,20,21,23,24,25,26,27,28,29,30,31,
%T A161373 33,34,35,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,
%U A161373 57,58,59,60,61,62,63,65
%N 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.
%C A161373 A161373 U A161374 = A000027.
%C A161373 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
%H A161373 H. v. Eitzen, <a href="http://www.von-eitzen.de/math/earlybird.pdf">Binary Early Birds</a> (2009).
%e A161373 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
%e A161373 20 ('10100') occurs at the joint of 18 and 19: the last 2 digits of '10010' and the first three of '10011'
%Y A161373 Cf. A116700, A161374, A296365.
%K A161373 easy,nonn
%O A161373 1,1
%A A161373 _Paolo P. Lava_ and _Giorgio Balzarotti_, Jun 08 2009
%E A161373 "Strictly" added to definition, offset corrected as customary for lists, 20 added by _Hagen von Eitzen_, Jun 27 2009