Links

[franktaw at netscape.net]

One thing I really wish people submitting sequences would do is take 
more time to look for related sequences in the database, and add links 
to them.  Especially, look for simpler variants of the same idea and 
link to those.  (Sometimes you'll find an even more interesting 
sequence that isn't in the database!)

For example, here's a random sample of ten sequences in the database 
(generated by WebCam), with comments about their links.

A024670 Distinct sums of cubes of 2 distinct positive integers.
Currently no links.
Obvious links:
Sums of 2 positive cubes (not necessarily distinct): A003325.
Sums of 3 distinct positive cubes: A024975.
Sums of distinct positive cubes: A003997.
Sums of 2 distinct non-negative cubes: not in OEIS, starts 
1,8,9,27,28,35,64.  [Submitted.]
Sums of 2 non-negative cubes: A004999.
Sums of 2 distinct positive squares: A004431.
and even: Cubes: A000578.

A070227 a(n)=sum(k=0,infinity,(k+n)!^n/((k+n)!*(k!^n)*exp(1))).
Currently no links.
There's nothing immediately obvious to me here, but I think there must 
be some similar things in the database.

A105027 [Long description, related to sloping binary numbers]
Currently 4 links, including A102370, the sloping binary numbers.
This looks fine.

A075341 a(1) = 1, a(2n) is the smallest composite number == 1 mod 
(a(2n-1)) and a(2n+1) is the smallest prime == 1 (mod a(2n)).
Link to A075450, which interchanges prime and composite in this 
description.
Obvious links:
Always look for prime: A061092.
Always look for composite: A061766.
Note that these don't have the initial 1 - you have to be careful when 
searching.

A101958 Indices of primes in sequence defined by A(0) = 23, A(n) = 
10*A(n-1) + 13 for n > 0.
Links to A000533: 10^n+1; A002275, repunits; and A102953, a(n)+1.
The sequence A is not in the database, but it doesn't really need to 
be.  (23, 243, 2443, 24443, ...).
Bleah.

A081334 sigma(2*n^2) modulo 4.
Currently no links.
Obvious link to sigma(2*n^2),  A065765.

A041308 Numerators of continued fraction convergents to sqrt(167).
Links to A041309, the denominators.
Obvious link to A010215, the continued fraction.
Also, this and adjacent sequences have the "cofr" keyword.  Shouldn't 
they have "frac" instead?

A074442 Number of 6-ary Lyndon words of length n with trace 3 and 
subtrace 2 over Z_6.
Currently has 23 links.  I think those are probably adequate.

A031519 Numbers n such that continue fraction for sqrt(n) has even 
period and central term 19.
Currently has no links.
Adjacent sequences are related.  Maybe there should be links.

A017154  (8n+7)^6.
Currently has no links.
Adjacent sequences are related.  Maybe there should be links.
Also 6th powers: A001014.

Franklin T. Adams-Watters

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