help needed in distinguishing two sequences

[franktaw at netscape.net]

A055039 can also be described as numbers whose base 4 representation 
ends in 3,2 followed by some number of zeros, while A044075 is numbers 
whose base 4 representation ends in 3,2 followed by some number of 
zeros, and includes no other 3,2.  So the difference, A124169, is 
numbers whose base 4 representation ends in 3,2 followed by some number 
of zeros, and includes at least one other 3,2.

This means that, in spite of the initial terms, asymptotically most 
members of A055039 are not in A044075.  In fact, A055039 has density 
1/12, while A044075 has density zero.

Franklin T. Adams-Watters


-----Original Message-----
From: njas at research.att.com

Dear Seqfans:  At present I have these two entries:
%I A055039
%S A055039 
14,30,46,56,62,78,94,110,120,126,142,158,174,184,190,206,222,224,
%T A055039 
238,248,254,270,286,302,312,318,334,350,366,376,382,398,414,430,
%U A055039 
440,446,462,478,480,494,504,510,526,542,558,568,574,590,606,622
%N A055039 Numbers of the form 2^(2i+1)*(8*j+7).
%C A055039 The numbers not of the form x^2+y^2+2z^2.
%C A055039 These are the numbers not occurring as norms in the 
face-centered
cubic lattice (cf. A004015).
%C A055039 Numbers of the form (16x^2+14)y^2. Also numbers of the form 
6x^2 +
8x^2(2y -1). (Steve Waterman).
...
%Y A055039 Equals twice A004215. Not the same as A044075.
...

and

%I A044075
%S A044075 14,30,46,56,62,78,94,110,120,126,142,158,174,184,190,206,222,
%T A044075 224,248,254,270,286,302,312,318,334,350,366,376,382,398,414,
%U A044075 430,440,446,462,478,480,504,510,526,542,558,568,574,590,606
%N A044075 Numbers n such that the string 3,2 occurs in the base 4
representation of n but not of n-1.
%C A044075 Not the same as A055039.
...

It appears that the first properly contains the second,
the numbers 238, 494, ... being in the first but not the second.

I will start a new entry, A124169, with 238,494,...
Could someone compute further terms (and double-check everything)?

Thanks

Neil

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