Finite Number Of Composites In Sequence?

[Leroy Quet]

I just submitted these two sequences.

%I A138244
%S A138244 1,2,5,7,11,17,25,37,47,61,79,101,127
%N A138244 a(1)=1. a(n) = smallest integer >
a(n-1) such that a(n) is coprime to (a(k)-a(k-1))
for all k, 2<=k<=n, and such that (a(n)-a(n-1))
doesn't equal (a(k)-a(k-1)) for any k, 2<=k<=n-1.
%C A138244 a(n+1)-a(n) = A138245(n)
%Y A138244 A138245
%O A138244 1
%K A138244 ,more,nonn,


%I A138245
%S A138245 1,3,2,4,6,8,12,10,14,18,22,26
%N A138245 a(n) = A138244(n+1) - A138244(n).
%e A138245 With the exception of the first two
terms, all terms of this sequence are even.
By definition, no integer occurs more than once
in this sequence.
%Y A138245 A138244
%O A138245 1
%K A138245 ,more,nonn,

I am curious. Are there only a finite number of
composites in sequence A138244?
(The only composite so far is the 25, of course.)

If the composite sequence is infinite and even if
it is finite but of significant length, could
someone please calculate the composites of
A138244 and submit the list to the EIS or email
them to me or seq.fan so I can submit them to the
EIS?

Thanks,
Leroy Quet




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