# [seqfan] Re: SImplified description of A161373 and A161374

franktaw at netscape.net franktaw at netscape.net
Fri Jun 12 16:11:16 CEST 2009

```But 22 is punctual.

-----Original Message-----
From: Hagen von Eitzen <hagen at von-eitzen.de>
...
3) All n with at least 3 1's in binary are early bird:
Write n in binary as 1.a.1.b.1.c where '.' denotes concatenation, a,b,c
are (possibly empty) strings and a and c consist only of 0's (i.e. we
have focused on the first, the second and the last 1).
3.1) Assume b contains at least one 0.
Then ingenearal x.b +1 = x.d for a string d with length(d)=length(b).
3.1.1) Assume length(c) > length(a).
Let m = 1.c.1.a.1.b. Then  m < n and m+1 = 1.c.1.a.1.d, hence n occurs
early at the junction of m and m+1.
3.1.2) Assume length(c) <= length(a).
Let m = 1.a.1.b < n, then m+1 =1.a.1.d begins with 1.c, hence n occurs
early at the junction of m and m+1.
3.2) Assume b consists only of 1's
3.2.1) Assume length(c)>=length(a).
Let m = 1.c.0.a.1.b, then m<n and m+1 begins with 1.c, hence n occurs
early at the junction of m and m+1.
3.2.2) Assume length(c) < length(a), esp. length(a)>0
Let m = 1.a.1.b < n, then m+1 begins with 1.c, hence n occurs early at
the junction of m and m+1.
...

```