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A278051 Let v = list of denominators of Farey series of order n (see A006843); let b(n) = Sum 1/(k+k'), where (k,k') are pairs of successive terms of v; a(n) = denominator of b(n). 4
2, 3, 10, 35, 252, 2772, 6435, 858, 680680, 12932920, 5290740, 121687020, 1029659400, 3088978200, 582272390700, 18050444111700, 128701918800, 25740383760, 70301729698200, 10043104242600, 109530094869795600, 523310453266801200, 51193413906534900, 481218090721428060 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
J. Lehner and M. Newman, Sums involving Farey fractions, Acta Arithmetica 15.2 (1969): 181-187. See Eq. (20).
EXAMPLE
The fractions b(n) are 1/2, 2/3, 9/10, 38/35, 347/252, 4189/2772, 11767/6435, 1733/858, 1548081/680680, 31464371/12932920, 14680543/5290740, 353517989/121687020, 3350216417/1029659400, 10571768267/3088978200, ...
MAPLE
Farey := proc(n) sort(convert(`union`({0}, {seq(seq(m/k, m=1..k), k=1..n)}), list)) end:
ans:=[];
for n from 1 to 30 do
t1:=denom(Farey(n));
t2:=add( 1/(t1[i]+t1[i+1]), i=1..nops(t1)-1);
ans:=[op(ans), t2];
od:
ans;
map(numer, ans); # A278050
map(denom, ans); # A278051
CROSSREFS
Sequence in context: A134959 A270367 A056607 * A060604 A075890 A296269
KEYWORD
nonn,frac
AUTHOR
N. J. A. Sloane, Nov 23 2016
STATUS
approved

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Last modified April 17 17:01 EDT 2024. Contains 371765 sequences. (Running on oeis4.)