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A245677
Numerator of sum of fractions A182972(k) / A182973(k) such that A182972(k) + A182973(k) = n.
5
1, 1, 11, 1, 79, 26, 339, 34, 5297, 62, 69071, 1165, 11723, 9844, 471181, 2625, 8960447, 73244, 8231001, 243757, 1031626241, 151100, 4178462515, 2651758, 10396147563, 11843614, 64166447971, 362476, 1989542332021, 97275764008, 1830230212061, 57286319768
OFFSET
3,3
COMMENTS
A182972(n) and A182973(n) provide an enumeration of positive rationals < 1 arranged by increasing sum of numerator and denominator then by increasing numerator;
a(n) = numerator(sum(A182972(k)/A182973(k): k such that A182972(k)+A182973(k)=n));
A245718(n) = floor(a(n)/A245678(n)).
LINKS
Paul Yiu, Recreational Mathematics, 24.3.1 Appendix: Two enumerations of the rational numbers in (0,1), page 633.
EXAMPLE
. | (num, den) = (A182973, A182973) | num(sum)| den(sum)| [sum]
. n | num/den, num + den = n | A245677 | A245678 | A245718
. ----+----------------------------------+---------+---------+--------
. 3 | 1/2 | 1 | 2 | 0
. 4 | 1/3 | 1 | 3 | 0
. 5 | 1/4, 2/3 | 11 | 12 | 0
. 6 | 1/5 | 1 | 5 | 0
. 7 | 1/6, 2/5, 3/4 | 79 | 60 | 1
. 8 | 1/7, 3/5 | 26 | 35 | 0
. 9 | 1/8, 2/7, 4/5 | 339 | 280 | 1
. 10 | 1/9, 3/7 | 34 | 63 | 0
. 11 | 1/10, 2/9, 3/8, 4/7, 5/6 | 5297 | 2520 | 2
. 12 | 1/11, 5/7 | 62 | 77 | 0
. 13 | 1/12, 2/11, 3/10, 4/9, 5/8, 6/7 | 69071 | 27720 | 2
. 14 | 1/13, 3/11, 5/9 | 1165 | 1287 | 0
. 15 | 1/14, 2/13, 4/11, 7/8 | 11723 | 8008 | 1
. 16 | 1/15, 3/13, 5/11, 7/9 | 9844 | 6435 | 1 .
PROG
(Haskell)
import Data.Ratio ((%), numerator)
a245677 n = numerator $ sum
[num % den | num <- [1 .. div n 2], let den = n - num, gcd num den == 1]
CROSSREFS
Cf. A245678 (denominator), A182972, A182973, A245718.
Sequence in context: A194039 A298084 A275304 * A182041 A086994 A305989
KEYWORD
nonn,frac
AUTHOR
Reinhard Zumkeller, Jul 30 2014
STATUS
approved