A161374 - OEIS

%I #24 Dec 14 2022 15:53:37

%S 0,1,2,4,8,10,16,22,32,36,64,128,136,256,512,528,1024,2048,2080,4096,

%T 8192,8256,16384,32768,32896,65536,131072,131328,262144,524288,524800,

%U 1048576,2097152,2098176,4194304,8388608,8390656,16777216,33554432

%N "Punctual" binary numbers. Complement of A161373.

%C A161373 U {a(n)} = A000027.

%C Whether or not 22 is punctual or early bird is a matter interpretation of "early occurrence" in the definition of A161373: 10110 occurs as the right 3 bits of 21 (10101) and the left 2 bits of 22 (10110) itself, which is ahead of the natural position, but not *completely* ahead of it. One can show (see weblink) the 22 is the only such case of doubt. [From _Hagen von Eitzen_, Jun 29 2009]

%H H. v. Eitzen, <a href="http://www.von-eitzen.de/math/earlybird.pdf">Binary Early Birds</a> (2009). [From _Hagen von Eitzen_, Jun 29 2009]

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,6,0,0,-8).

%F From _Hagen von Eitzen_, Jun 29 2009: (Start)

%F G.f.: (1+x+2x^2)/(2-8x^3) + x/(2-4x^3) -1/2 -x + x^4 + 4x^5 + 2x^6 + 6x^7 + 6x^8

%F If q>=3 then a(3q) = 2^(2q-1), a(3q+1) = 2^(2q-1) + 2^(q-1), a(3q+2) = 2^(2q). (End)

%F a(n) = A083655(n-2) for n>=9. - _Alois P. Heinz_, Dec 14 2022

%Y Cf. A083655, A116700, A161373.

%K nonn,easy

%O 1,3

%A _Paolo P. Lava_ and _Giorgio Balzarotti_, Jun 08 2009

%E Offset corrected as customary for lists, 20 removed by _Hagen von Eitzen_, Jun 27 2009

%E More terms from _Hagen von Eitzen_, Jun 29 2009