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A214803 Frobenius numbers of numerators and denominators of rational numbers in order of their canonical enumeration.

%I A214803 #7 Feb 16 2025 08:33:18
%S A214803 -1,-1,1,-1,5,-1,3,7,11,-1,19,-1,5,11,17,23,29,-1,13,27,41,-1,7,23,31,
%T A214803 47,55,-1,17,53,71,-1,9,19,29,39,49,59,69,79,89,-1,43,65,109,-1,11,23,
%U A214803 35,47,59,71,83,95,107,119,131,-1,25,51,103,129,155,-1,13
%N A214803 Frobenius numbers of numerators and denominators of rational numbers in order of their canonical enumeration.
%C A214803 a(n) = A020652(n) * A038567(n) - A020652(n) - A038567(n);
%C A214803 for n > 1: a(A015614(n)) = A165900(n-1);
%C A214803 a(A002088(n)) = -1.
%H A214803 Reinhard Zumkeller, <a href="/A214803/b214803.txt">Table of n, a(n) for n = 1..10000</a>
%H A214803 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FrobeniusNumber.html">Frobenius Number</a>.
%H A214803 Wikipedia, <a href="http://en.wikipedia.org/wiki/Coin_problem">Coin problem</a>
%o A214803 (Haskell)
%o A214803 a214803 n = a214803_list !! (n-1)
%o A214803 a214803_list = [x * y - x - y | y <- [1..], x <- [1..y-1], gcd x y == 1]
%K A214803 sign
%O A214803 1,5
%A A214803 _Reinhard Zumkeller_, Jul 29 2012