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).
Original entry on oeis.org
2, 3, 10, 35, 252, 2772, 6435, 858, 680680, 12932920, 5290740, 121687020, 1029659400, 3088978200, 582272390700, 18050444111700, 128701918800, 25740383760, 70301729698200, 10043104242600, 109530094869795600, 523310453266801200, 51193413906534900, 481218090721428060
Offset: 1
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, ...
-
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
A278047
Let v = list of denominators of Farey series of order n (see A006843); let b(n) = Sum 1/(k*k'*(k+k')), where (k,k') are pairs of successive terms of v; a(n) = numerator of b(n).
Original entry on oeis.org
1, 1, 7, 4, 37, 53, 707, 85, 179077, 289613, 379721, 641671, 62836087, 35819033, 6367281023, 55181728027, 13442946373, 490167893, 596530310479, 576997238399, 116144361532321, 4931206160615, 164890340129357, 1514840590670747, 10181612956306486603, 3295813969039399097
Offset: 1
The fractions b(n) are 1/2, 1/3, 7/30, 4/21, 37/252, 53/396, 707/6435, 85/858, 179077/2042040, 289613/3527160, 379721/5290740, 641671/9360540, 62836087/1029659400, 35819033/617795640, ...
-
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 50 do
t1:=denom(Farey(n));
t2:=add( 1/(t1[i]*t1[i+1]*(t1[i]+t1[i+1])),i=1..nops(t1)-1);
ans:=[op(ans),t2];
od:
ans;
map(numer,ans); # A278047
map(denom,ans); # A278048
A278048
Let v = list of denominators of Farey series of order n (see A006843); let b(n) = Sum 1/(k*k'*(k+k')), where (k,k') are pairs of successive terms of v; a(n) = denominator of b(n).
Original entry on oeis.org
2, 3, 30, 21, 252, 396, 6435, 858, 2042040, 3527160, 5290740, 9360540, 1029659400, 617795640, 116454478140, 1061790830100, 283144221360, 10644519600, 14060345939640, 14060345939640, 2960272834318800, 130015019445168, 4653946718775900, 43747099156493460
Offset: 1
The fractions b(n) are 1/2, 1/3, 7/30, 4/21, 37/252, 53/396, 707/6435, 85/858, 179077/2042040, 289613/3527160, 379721/5290740, 641671/9360540, 62836087/1029659400, 35819033/617795640, ...
-
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 50 do
t1:=denom(Farey(n));
t2:=add( 1/(t1[i]*t1[i+1]*(t1[i]+t1[i+1])),i=1..nops(t1)-1);
ans:=[op(ans),t2];
od:
ans;
map(numer,ans); # A278047
map(denom,ans); # A278048
A278050
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) = numerator of b(n).
Original entry on oeis.org
1, 2, 9, 38, 347, 4189, 11767, 1733, 1548081, 31464371, 14680543, 353517989, 3350216417, 10571768267, 2114915577977, 69039991480573, 538250871701, 110983833313, 328448743696081, 48484885139543, 553270527392631611, 2736415713954900433, 286367762285513933, 2754025786313797907
Offset: 1
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, ...
-
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
A278052
Let v = list of denominators of Farey series of order n (see A006843); let b(n) = Sum k*k'/(k+k'), where (k,k') are pairs of successive terms of v; a(n) = numerator of b(n).
Original entry on oeis.org
1, 4, 39, 52, 4069, 8573, 258017, 46639, 53371999, 113518551, 768140741, 1560819091, 242830653007, 169134016817, 38186305937387, 408881289764107, 143220706672837, 41293923006131, 9928250098118791, 10936700271572951, 97615258031147892517, 643700119549549507, 62211198375587838727
Offset: 1
The fractions b(n) are 1/2, 4/3, 39/10, 52/7, 4069/252, 8573/396, 258017/6435, 46639/858, 53371999/680680, 113518551/1175720, 768140741/5290740, 1560819091/9360540, 242830653007/1029659400, 169134016817/617795640, 38186305937387/116454478140, ...
-
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( t1[i]*t1[i+1]/(t1[i]+t1[i+1]), i=1..nops(t1)-1);
od:
ans;
map(numer,ans); # A278052
map(denom,ans); # A278561
A278561
Let v = list of denominators of Farey series of order n (see A006843); let b(n) = Sum k*k'/(k+k'), where (k,k') are pairs of successive terms of v; a(n) = denominator of b(n).
Original entry on oeis.org
2, 3, 10, 7, 252, 396, 6435, 858, 680680, 1175720, 5290740, 9360540, 1029659400, 617795640, 116454478140, 1061790830100, 283144221360, 74511637200, 14060345939640, 14060345939640, 109530094869795600, 650075097225840, 51193413906534900, 481218090721428060
Offset: 1
The fractions b(n) are 1/2, 4/3, 39/10, 52/7, 4069/252, 8573/396, 258017/6435, 46639/858, 53371999/680680, 113518551/1175720, 768140741/5290740, 1560819091/9360540, 242830653007/1029659400, 169134016817/617795640, 38186305937387/116454478140, ...
-
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( t1[i]*t1[i+1]/(t1[i]+t1[i+1]), i=1..nops(t1)-1);
od:
ans;
map(numer,ans); # A278052
map(denom,ans); # A278561
Showing 1-6 of 6 results.