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A251608 Lexicographically earliest subsequence of the Fibonacci numbers (cf. A000045), such that gcd(a(n-2), a(n)) > 1 and gcd(a(n-1), a(n)) = 1.

%I A251608 #10 Aug 01 2019 03:47:45
%S A251608 2,3,8,21,34,987,2584,6765,10946,75025,196418,9227465,14930352,
%T A251608 7778742049,20365011074,225851433717,365435296162,10610209857723,
%U A251608 27777890035288,72723460248141,117669030460994,3416454622906707,8944394323791464,23416728348467685
%N A251608 Lexicographically earliest subsequence of the Fibonacci numbers (cf. A000045), such that gcd(a(n-2), a(n)) > 1 and gcd(a(n-1), a(n)) = 1.
%H A251608 Reinhard Zumkeller, <a href="/A251608/b251608.txt">Table of n, a(n) for n = 1..1000</a>
%e A251608    n |   a(n) | pos in A000045 | pos in A098550
%e A251608   ---+--------+----------------+----------------
%e A251608    1 |      2 |              3 |              2
%e A251608    2 |      3 |              4 |              3
%e A251608    3 |      8 |              6 |              6
%e A251608    4 |     21 |              8 |             17
%e A251608    5 |     34 |              9 |             35
%e A251608    6 |    987 |             16 |            776
%e A251608    7 |   2584 |             18 |           2755
%e A251608    8 |   6765 |             20 |           5707
%e A251608    9 |  10946 |             21 |          11652
%e A251608   10 |  75025 |             25 |          66539
%o A251608 (Haskell)
%o A251608 a251608 n = a251608_list !! (n-1)
%o A251608 a251608_list = 2 : 3 : f 2 3 (drop 5 a000045_list) where
%o A251608    f u v (w:ws) = if gcd u w > 1 && gcd v w == 1
%o A251608                      then w : f v w ws else f u v ws
%Y A251608 Cf. A000045, A098550, A249357.
%K A251608 nonn
%O A251608 1,1
%A A251608 _Reinhard Zumkeller_, Dec 05 2014