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Let S be the sequence of rational numbers generated by these rules: 1 is in S, and if u/v is in S (with gcd(u, v) = 1), then (u+1)/v and u/(v+1) are in S, and duplicates are deleted as they occur; a(n) = the denominator of the n-th term of S.
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%I #9 Oct 05 2017 09:54:32

%S 1,1,2,1,3,1,2,3,4,1,5,1,2,5,6,1,3,5,7,1,2,4,5,7,8,1,3,7,9,1,2,3,4,7,

%T 8,9,10,1,5,7,11,1,2,5,6,7,8,11,12,1,3,5,3,4,9,11,13,1,2,4,11,13,14,1,

%U 3,5,11,13,15,1,2,3,4,5,6,11,12,13,14,15,16

%N Let S be the sequence of rational numbers generated by these rules: 1 is in S, and if u/v is in S (with gcd(u, v) = 1), then (u+1)/v and u/(v+1) are in S, and duplicates are deleted as they occur; a(n) = the denominator of the n-th term of S.

%C See A293247 for the corresponding numerators, and additional comments.

%H Rémy Sigrist, <a href="/A293248/b293248.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A293248/a293248.gp.txt">PARI program for A293248</a>

%e S(1) = 1 by definition; so a(1) = 1.

%e (1+1)/1 = 2 has not yet occurred; so S(2) = 2 and a(2) = 1.

%e 1/(1+1) = 1/2 has not yet occurred; so S(3) = 1/2 and a(3) = 2.

%e (2+1)/1 = 3 has not yet occurred; so S(4) = 3 and a(4) = 1.

%e 2/(1+1) = 1 has already occurred.

%o (PARI) See Links section.

%Y Cf. A293247.

%K nonn,frac

%O 1,3

%A _Rémy Sigrist_, Oct 03 2017