A161374 "Punctual" binary numbers. Complement of A161373.

0, 1, 2, 4, 8, 10, 16, 22, 32, 36, 64, 128, 136, 256, 512, 528, 1024, 2048, 2080, 4096, 8192, 8256, 16384, 32768, 32896, 65536, 131072, 131328, 262144, 524288, 524800, 1048576, 2097152, 2098176, 4194304, 8388608, 8390656, 16777216, 33554432

Offset: 1

Author

Paolo P. Lava and Giorgio Balzarotti, Jun 08 2009

Keywords

• nonn
• easy

Comments

A161373 U {a(n)} = A000027.

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]

Links

• H. v. Eitzen, Binary Early Birds (2009). [From _Hagen von Eitzen_, Jun 29 2009]
• Index entries for linear recurrences with constant coefficients, signature (0,0,6,0,0,-8).

Crossrefs

Cf. A083655, A116700, A161373.

Formula

From Hagen von Eitzen, Jun 29 2009: (Start)

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

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

a(n) = A083655(n-2) for n>=9. - Alois P. Heinz, Dec 14 2022

Extensions

Offset corrected as customary for lists, 20 removed by Hagen von Eitzen, Jun 27 2009

More terms from Hagen von Eitzen, Jun 29 2009