A113910 and Lesser of twin primes

[Creighton Dement]

Dear Seqfans, 

In reference to 
http://public.research.att.com/~njas/sequences/A113910

conjecture: a(n+4) = A001359(n+2) for all n.
A001359:  Lesser of twin primes. 

An immediate corollary of the above would be: 9 is the only composite
term of the  sequence... perhaps this is somehow easier to prove.  

Note: for n = 3, 4, 5, 6, 7, 8, 9, 10 ... 

((Lucas(n+1) - 2*A006206(n+2))/(A006206(n+2) - A006206(n))) = [3, 7, 5,
19/3, 31/4, 9, 87/10, 149/14, 11, 135/11, 663/50, 1094/77, 1787/120,
2939/181, 17, 7849/434, 12799/672, 20894/1041, 34031/1622, 55469/2514,
45131/1962, 146921/6115, 238915/9554, 194252/7465, 631347/23386,
1025917/36617, 29, 2706059/90178, 4393211/141710, 3565643/111405,
11573003/350702] 

or 

= [3.0, 7.0, 5.0, 6.333333333, 7.750000000, 9.0, 8.700000000,
10.64285714, 11.0, 12.27272727, 13.26000000, 14.20779221, 14.89166667,
16.23756906, 17.0, 18.08525346, 19.04613095, 20.07108549, 20.98088779,
22.06404137, 23.00254842, 24.02632870, 25.00680343, 26.02170127,
26.99679295, 28.01750553, 29.0, 30.00797312, 31.00141839, 32.00613078,
32.99953522}
 

Sincerely, 
Creighton


-It's a shame when the girl of your dreams would still rather be with
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