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 A182972 Numerators of positive rationals < 1 arranged by increasing sum of numerator and denominator then by increasing numerator. 11
 1, 1, 1, 2, 1, 1, 2, 3, 1, 3, 1, 2, 4, 1, 3, 1, 2, 3, 4, 5, 1, 5, 1, 2, 3, 4, 5, 6, 1, 3, 5, 1, 2, 4, 7, 1, 3, 5, 7, 1, 2, 3, 4, 5, 6, 7, 8, 1, 5, 7, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 3, 7, 9, 1, 2, 4, 5, 8, 10, 1, 3, 5, 7, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 1, 5, 7, 11, 1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 1, 3, 5, 7, 9, 11 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS A023022(n) and A245677(n) give number and numerator of sum of fractions a(k)/A182973(k) such that a(k)+A182973(k) = n. - Reinhard Zumkeller, Jul 30 2014 REFERENCES S. Cook, Problem 511: An Enumeration Problem, Journal of Recreational Mathematics, Vol. 9:2 (1976-77), 137. Solution by the Problem Editor, JRM, Vol. 10:2 (1977-78), 122-123. R. K. Guy, Unsolved Problems in Number Theory (UPINT), Section D11. LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 Paul Yiu, Recreational Mathematics, 24.3.1 Appendix: Two enumerations of the rational numbers in (0,1), page 633. EXAMPLE Positive fractions < 1 listed by increasing sum of numerator and denominator, and by increasing numerator for equal sums: 1/2 1/3 1/4 2/3 1/5 1/6 2/5 3/4 1/7 3/5 1/8 2/7 4/5 1/9 3/7 1/10 2/9 3/8 4/7 5/6 1/11 5/7 1/12 2/11 3/10 4/9 5/8 6/7 1/13 3/11 5/9 1/14 2/13 4/11 7/8 1/15 3/13 5/11 7/9 1/16 2/15 3/14 4/13 5/12 6/11 7/10 8/9 1/17 5/13 7/11 1/18 2/17 3/16 4/15 5/14 6/13 7/12 8/11 9/10 1/19 3/17 7/13 9/11 (this is A182972/A182973). MAPLE t1:=[]; for n from 2 to 40 do t1:=[op(t1), 1/(n-1)]; for i from 2 to floor((n-1)/2) do    if gcd(i, n-i)=1 then t1:=[op(t1), i/(n-i)]; fi; od: od: t1; MATHEMATICA t1={}; For[n=2, n <= 40, n++, AppendTo[t1, 1/(n-1)]; For[i=2, i <= Floor[(n-1)/2], i++, If[GCD[i, n-i] == 1, AppendTo[t1, i/(n-i)]]]]; t1 // Numerator // Rest (* Jean-François Alcover, Jan 20 2015, translated from Maple *) PROG (PASCAL) program a182972; var   num, den, n: longint; function gcd(i, j: longint):longint; begin   repeat     if i>j then i:=i mod j else j:=j mod i;   until (i=0) or (j=0);   if i=0 then gcd:=j else gcd:=i; end; begin   num:=1; den:=1; n:=0;   repeat     repeat       inc(num); dec(den);       if num>=den then       begin         inc(den, num); num:=1;       end;     until gcd(num, den)=1;     inc(n); writeln(n, ' ', num);   until n=100000; end. (Haskell) a182972 n = a182972_list !! (n-1) a182972_list = map fst \$ concatMap q [3..] where    q x = [(num, den) | num <- [1 .. div x 2],                        let den = x - num, gcd num den == 1] -- Reinhard Zumkeller, Jul 29 2014 CROSSREFS Cf. A020652, A038567, A182973-A182976. Cf. A023022, A245677, A245678, A245718. Sequence in context: A025830 A083796 A037039 * A153452 A090680 A133771 Adjacent sequences:  A182969 A182970 A182971 * A182973 A182974 A182975 KEYWORD nonn,easy,frac,nice AUTHOR William Rex Marshall, Dec 16 2010 EXTENSIONS Corrected by William Rex Marshall, Aug 12 2013 STATUS approved

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Last modified February 26 05:19 EST 2020. Contains 332276 sequences. (Running on oeis4.)