A137365: correct terms?

[Richard Mathar]

I just submitted these two sequences:

%S A139317 2,3,7,5,11,13,29,17,19,31,23,37
%N A139317 a(n) = the smallest value of the form
n*k +1, k = positive integer, that is coprime to
all the previous terms of this sequence.
%C A139317 Are there any composites in this
sequence? If not, is this sequence a permutation
of the primes?
%e A139317 For a(7) we check: 7*1 +1= 8, which is
not coprime to a(1)=2. 7*2 +1= 15, which is not
coprime to either a(2)=3 or to a(4)=5. 7*3 +1 =
22, which is not coprime to either a(1)=2 or to
a(5)=11. But 7*4+1 = 29, which is coprime to
terms a(1) through a(6). So a(7) = 29.
%Y A139317 A139318,A139319
%O A139317 1
%K A139317 ,more,nonn,

%S A139319 1,1,2,3,19,5,13,7,17,29,43,11
%N A139319 a(n) = the smallest value of the form
n*k -1, k = positive integer, that is coprime to
all the previous terms of this sequence. a(1)=1.
%C A139319 Are there any composites in this
sequence? If not, is this sequence, with the
exception of terms a(1) and a(2), a permutation
of the primes?
%e A139319 For a(10) we check: 10*1 -1= 9, which
is not coprime to a(4)=3. 10*2 -1= 19, which is
not coprime to a(5)=19. But 10*3 -1 = 29, which
is coprime to terms a(1) through a(9). So a(10) =
29.
%Y A139319 A139317,A1393120
%O A139319 1
%K A139319 ,more,nonn,

A139318 and A139320 are the sequences of k's for
sequences A139317 and A139319.


See the C-lines for the questions I have.
(Perhaps simply calculating a few more terms will
answer if there are indeed composites, even if it
does not prove that the sequences contain all
primes.)

Thanks,
Leroy Quet



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