A002530 -id:A002530 - cp's OEIS frontend

A041263 Denominators of continued fraction convergents to sqrt(143).

1, 1, 23, 24, 551, 575, 13201, 13776, 316273, 330049, 7577351, 7907400, 181540151, 189447551, 4349386273, 4538833824, 104203730401, 108742564225, 2496540143351, 2605282707576, 59812759710023, 62418042417599, 1433009692897201, 1495427735314800

Offset: 0

N. J. A. Sloane

The following remarks assume an offset of 1. This is the sequence of Lehmer numbers U_n(sqrt(R),Q) for the parameters R = 22 and Q = -1; it is a strong divisibility sequence, that is, gcd(a(n),a(m)) = a(gcd(n,m)) for all positive integers n and m. Consequently, this is a divisibility sequence: if n divides m then a(n) divides a(m). - Peter Bala, May 28 2014

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Eric W. Weisstein, MathWorld: Lehmer Number
Index entries for linear recurrences with constant coefficients, signature (0,24,0,-1).

Cf. A041262, A002530.

I:=[1,1,23,24]; [n le 4 select I[n] else 24*Self(n-2)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Dec 14 2013

Denominator[Convergents[Sqrt[143], 30]] (* or *) CoefficientList[Series[(1 + x - x^2)/(x^4 - 24 x^2 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 14 2013 *)

G.f.: (1 + x - x^2)/(x^4 - 24*x^2 + 1). - Vincenzo Librandi, Dec 14 2013
a(n) = 24*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 14 2013
From Peter Bala, May 28 2014: (Start)
The following remarks assume an offset of 1.
Let alpha = ( sqrt(22) + sqrt(26) )/2 and beta = ( sqrt(22) - sqrt(26) )/2 be the roots of the equation x^2 - sqrt(22)*x - 1 = 0. Then a(n) = (alpha^n - beta^n)/(alpha - beta) for n odd, while a(n) = (alpha^n - beta^n)/(alpha^2 - beta^2) for n even.
a(n) = Product_{k = 1..floor((n-1)/2)} ( 22 + 4*cos^2(k*Pi/n) ).
Recurrence equations: a(0) = 0, a(1) = 1 and for n >= 1, a(2*n) = a(2*n - 1) + a(2*n - 2) and a(2*n + 1) = 22*a(2*n) + a(2*n - 1). (End)

More terms from Vincenzo Librandi, Dec 14 2013

A041311 Denominators of continued fraction convergents to sqrt(168).

Original entry on oeis.org

1, 1, 25, 26, 649, 675, 16849, 17524, 437425, 454949, 11356201, 11811150, 294823801, 306634951, 7654062625, 7960697576, 198710804449, 206671502025, 5158826853049, 5365498355074, 133930787374825, 139296285729899, 3477041644892401, 3616337930622300

Offset: 0

N. J. A. Sloane

The following remarks assume an offset of 1. This is the sequence of Lehmer numbers U_n(sqrt(R),Q) for the parameters R = 24 and Q = -1; it is a strong divisibility sequence, that is, gcd(a(n),a(m)) = a(gcd(n,m)) for all positive integers n and m. Consequently, this is a divisibility sequence: if n divides m then a(n) divides a(m). - Peter Bala, May 28 2014

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Eric W. Weisstein, MathWorld: Lehmer Number
Index entries for linear recurrences with constant coefficients, signature (0,26,0,-1).

Cf. A041310, A040155, A002530.

I:=[1,1,25,26]; [n le 4 select I[n] else 26*Self(n-2)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Dec 15 2013

Denominator[Convergents[Sqrt[168], 30]] (* Vincenzo Librandi, Dec 15 2013 *)

G.f.: -(x^2-x-1) / (x^4-26*x^2+1). - Colin Barker, Nov 15 2013
a(n) = 26*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 15 2013
From Peter Bala, May 28 2014: (Start)
The following remarks assume an offset of 1.
Let alpha = sqrt(6) + sqrt(7) and beta = sqrt(6) - sqrt(7) be the roots of the equation x^2 - sqrt(24)*x - 1 = 0. Then a(n) = (alpha^n - beta^n)/(alpha - beta) for n odd, while a(n) = (alpha^n - beta^n)/(alpha^2 - beta^2) for n even.
a(n) = Product_{k = 1..floor((n-1)/2)} ( 24 + 4*cos^2(k*Pi/n) ).
Recurrence equations: a(0) = 0, a(1) = 1 and for n >= 1, a(2*n) = a(2*n - 1) + a(2*n - 2) and a(2*n + 1) = 24*a(2*n) + a(2*n - 1). (End)

More terms from Colin Barker, Nov 15 2013

A041363 Denominators of continued fraction convergents to sqrt(195).

Original entry on oeis.org

1, 1, 27, 28, 755, 783, 21113, 21896, 590409, 612305, 16510339, 17122644, 461699083, 478821727, 12911063985, 13389885712, 361048092497, 374437978209, 10096435525931, 10470873504140, 282339146633571, 292810020137711, 7895399670214057, 8188209690351768

Offset: 0

N. J. A. Sloane

The following remarks assume an offset of 1. This is the sequence of Lehmer numbers U_n(sqrt(R),Q) for the parameters R = 26 and Q = -1; it is a strong divisibility sequence, that is, gcd(a(n),a(m)) = a(gcd(n,m)) for all positive integers n and m. Consequently, this is a divisibility sequence: if n divides m then a(n) divides a(m). - Peter Bala, May 28 2014

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Eric W. Weisstein, MathWorld: Lehmer Number
Index entries for linear recurrences with constant coefficients, signature (0,28,0,-1).

Cf. A041362, A040181, A002530.

I:=[1,1,27,28]; [n le 4 select I[n] else 28*Self(n-2)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Dec 16 2013

Denominator[Convergents[Sqrt[195], 30]] (* Vincenzo Librandi, Dec 16 2013 *)
LinearRecurrence[{0,28,0,-1},{1,1,27,28},30] (* Harvey P. Dale, Dec 04 2022 *)

G.f.: -(x^2-x-1) / (x^4-28*x^2+1). - Colin Barker, Nov 16 2013
a(n) = 28*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 16 2013
From Peter Bala, May 28 2014: (Start)
The following remarks assume an offset of 1.
Let alpha = ( sqrt(26) + sqrt(30) )/2 and beta = ( sqrt(26) - sqrt(30) )/2 be the roots of the equation x^2 - sqrt(26)*x - 1 = 0. Then a(n) = (alpha^n - beta^n)/(alpha - beta) for n odd, while a(n) = (alpha^n - beta^n)/(alpha^2 - beta^2) for n even.
a(n) = Product_{k = 1..floor((n-1)/2)} ( 26 + 4*cos^2(k*Pi/n) ).
Recurrence equations: a(0) = 0, a(1) = 1 and for n >= 1, a(2*n) = a(2*n - 1) + a(2*n - 2) and a(2*n + 1) = 26*a(2*n) + a(2*n - 1). (End)

More terms from Colin Barker, Nov 16 2013

A041419 Denominators of continued fraction convergents to sqrt(224).

Original entry on oeis.org

1, 1, 29, 30, 869, 899, 26041, 26940, 780361, 807301, 23384789, 24192090, 700763309, 724955399, 20999514481, 21724469880, 629284671121, 651009141001, 18857540619149, 19508549760150, 565096933903349, 584605483663499, 16934050476481321, 17518655960144820

Offset: 0

N. J. A. Sloane

The following remarks assume an offset of 1. This is the sequence of Lehmer numbers U_n(sqrt(R),Q) for the parameters R = 28 and Q = -1; it is a strong divisibility sequence, that is, gcd(a(n),a(m)) = a(gcd(n,m)) for all positive integers n and m. Consequently, this is a divisibility sequence: if n divides m then a(n) divides a(m). - Peter Bala, May 28 2014

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Eric W. Weisstein, MathWorld: Lehmer Number
Index entries for linear recurrences with constant coefficients, signature (0,30,0,-1).

Cf. A041418, A040209, A002530.

I:=[1,1,29,30]; [n le 4 select I[n] else 30*Self(n-2)-Self(n-4): n in [1..100]]; // Vincenzo Librandi, Dec 17 2013

Denominator[Convergents[Sqrt[224], 30]] (* Harvey P. Dale, May 07 2012 *)
CoefficientList[Series[(1 + x - x^2)/(x^4 - 30 x^2 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 17 2013 *)

G.f.: -(x^2-x-1) / (x^4-30*x^2+1). - Colin Barker, Nov 17 2013
a(n) = 30*a(n-2) - a(n-4) for n > 3. - Vincenzo Librandi, Dec 17 2013
From Peter Bala, May 28 2014: (Start)
The following remarks assume an offset of 1.
Let alpha = sqrt(7) + 2*sqrt(2) and beta = sqrt(7) - 2*sqrt(2) be the roots of the equation x^2 - sqrt(28)*x - 1 = 0. Then a(n) = (alpha^n - beta^n)/(alpha - beta) for n odd, while a(n) = (alpha^n - beta^n)/(alpha^2 - beta^2) for n even.
a(n) = Product_{k = 1..floor((n-1)/2)} ( 28 + 4*cos^2(k*Pi/n) ).
Recurrence equations: a(0) = 0, a(1) = 1 and for n >= 1, a(2*n) = a(2*n - 1) + a(2*n - 2) and a(2*n + 1) = 28*a(2*n) + a(2*n - 1). (End)

More terms from Colin Barker, Nov 17 2013

A041479 Denominators of continued fraction convergents to sqrt(255).

Original entry on oeis.org

1, 1, 31, 32, 991, 1023, 31681, 32704, 1012801, 1045505, 32377951, 33423456, 1035081631, 1068505087, 33090234241, 34158739328, 1057852414081, 1092011153409, 33818187016351, 34910198169760

Offset: 0

N. J. A. Sloane

The following remarks assume an offset of 1. This is the sequence of Lehmer numbers U_n(sqrt(R),Q) for the parameters R = 30 and Q = -1; it is a strong divisibility sequence, that is, gcd(a(n),a(m)) = a(gcd(n,m)) for all positive integers n and m. Consequently, this is a divisibility sequence: if n divides m then a(n) divides a(m). - Peter Bala, May 28 2014

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Eric W. Weisstein, MathWorld: Lehmer Number
Index entries for linear recurrences with constant coefficients, signature (0,32,0,-1).

Cf. A041478, A176110, A002530.

Denominator[Convergents[Sqrt[255],30]] (* or *) LinearRecurrence[ {0,32,0,-1},{1,1,31,32},30] (* Harvey P. Dale, Jan 19 2013 *)
CoefficientList[Series[- (x^2 - x - 1)/(x^4 - 32 x^2 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 25 2013 *)

From Colin Barker, Jul 16 2012: (Start)
a(n) = 32*a(n-2) - a(n-4).
G.f.: -(x^2-x-1)/(x^4-32*x^2+1). (End)
From Peter Bala, May 28 2014: (Start)
The following remarks assume an offset of 1.
Let alpha = ( sqrt(30) + sqrt(34) )/2 and beta = ( sqrt(30) - sqrt(34) )/2 be the roots of the equation x^2 - sqrt(30)*x - 1 = 0. Then a(n) = (alpha^n - beta^n)/(alpha - beta) for n odd, while a(n) = (alpha^n - beta^n)/(alpha^2 - beta^2) for n even.
a(n) = Product_{k = 1..floor((n-1)/2)} ( 30 + 4*cos^2(k*Pi/n) ).
Recurrence equations: a(0) = 0, a(1) = 1 and for n >= 1, a(2*n) = a(2*n - 1) + a(2*n - 2) and a(2*n + 1) = 30*a(2*n) + a(2*n - 1). (End)

A041543 Denominators of continued fraction convergents to sqrt(288).

Original entry on oeis.org

1, 1, 33, 34, 1121, 1155, 38081, 39236, 1293633, 1332869, 43945441, 45278310, 1492851361, 1538129671, 50713000833, 52251130504, 1722749176961, 1775000307465, 58522759015841, 60297759323306, 1988051057361633, 2048348816684939, 67535213191279681

Offset: 0

N. J. A. Sloane

The following remarks assume an offset of 1. This is the sequence of Lehmer numbers U_n(sqrt(R),Q) for the parameters R = 32 and Q = -1; it is a strong divisibility sequence, that is, gcd(a(n),a(m)) = a(gcd(n,m)) for all positive integers n and m. Consequently, this is a divisibility sequence: if n divides m then a(n) divides a(m). - Peter Bala, May 28 2014

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Eric W. Weisstein, MathWorld: Lehmer Number
Index entries for linear recurrences with constant coefficients, signature (0,34,0,-1).

Cf. A041542, A040271, A002530.

I:=[1,1,33,34]; [n le 4 select I[n] else 34*Self(n-2)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Dec 20 2013

Denominator[Convergents[Sqrt[288], 30]] (* Vincenzo Librandi, Dec 20 2013 *)

G.f.: -(x^2-x-1) / ((x^2-6*x+1)*(x^2+6*x+1)). - Colin Barker, Nov 18 2013
a(n) = 34*a(n-2) - a(n-4) for n > 3. - Vincenzo Librandi, Dec 20 2013
From Peter Bala, May 28 2014: (Start)
The following remarks assume an offset of 1.
Let alpha = 2*sqrt(2) + 3 and beta = 2*sqrt(2) - 3 be the roots of the equation x^2 - sqrt(32)*x - 1 = 0. Then a(n) = (alpha^n - beta^n)/(alpha - beta) for n odd, while a(n) = (alpha^n - beta^n)/(alpha^2 - beta^2) for n even.
a(n) = Product_{k = 1..floor((n-1)/2)} ( 32 + 4*cos^2(k*Pi/n) ).
Recurrence equations: a(0) = 0, a(1) = 1 and for n >= 1, a(2*n) = a(2*n - 1) + a(2*n - 2) and a(2*n + 1) = 32*a(2*n) + a(2*n - 1). (End)

More terms from Colin Barker, Nov 18 2013

A041683 Denominators of continued fraction convergents to sqrt(360).

Original entry on oeis.org

1, 1, 37, 38, 1405, 1443, 53353, 54796, 2026009, 2080805, 76934989, 79015794, 2921503573, 3000519367, 110940200785, 113940720152, 4212806126257, 4326746846409, 159975692596981, 164302439443390, 6074863512559021, 6239165952002411

Offset: 0

N. J. A. Sloane

The following remarks assume an offset of 1. This is the sequence of Lehmer numbers U_n(sqrt(R),Q) for the parameters R = 36 and Q = -1; it is a strong divisibility sequence, that is, gcd(a(n),a(m)) = a(gcd(n,m)) for all positive integers n and m. Consequently, this is a divisibility sequence: if n divides m then a(n) divides a(m). - Peter Bala, May 28 2014

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Eric W. Weisstein, MathWorld: Lehmer Number
Index entries for linear recurrences with constant coefficients, signature (0,38,0,-1).

Cf. A041682, A040341, A002530, A005668.

I:=[1,1,37,38]; [n le 4 select I[n] else 38*Self(n-2)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Dec 22 2013

Denominator[Convergents[Sqrt[360], 30]] (* Vincenzo Librandi, Dec 22 2013 *)

G.f.: -(x^2-x-1) / ((x^2-6*x-1)*(x^2+6*x-1)). - Colin Barker, Nov 21 2013
a(n) = 38*a(n-2) - a(n-4) for n > 3. - Vincenzo Librandi, Dec 22 2013
From Peter Bala, May 28 2014: (Start)
The following remarks assume an offset of 1.
Let alpha = 3 + sqrt(10) and beta = 3 - sqrt(10) be the roots of the equation x^2 - 6*x - 1 = 0. Then a(n) = (alpha^n - beta^n)/(alpha - beta) for n odd, while a(n) = (alpha^n - beta^n)/(alpha^2 - beta^2) for n even.
a(n) = A005668(n+1) for n even; a(n) = 1/6*A005668(n+1) for n odd.
a(n) = Product_{k = 1..floor((n-1)/2)} ( 36 + 4*cos^2(k*Pi/n) ).
Recurrence equations: a(0) = 0, a(1) = 1 and for n >= 1, a(2*n) = a(2*n - 1) + a(2*n - 2) and a(2*n + 1) = 36*a(2*n) + a(2*n - 1). (End)

More terms from Colin Barker, Nov 21 2013

A041759 Denominators of continued fraction convergents to sqrt(399).

Original entry on oeis.org

1, 1, 39, 40, 1559, 1599, 62321, 63920, 2491281, 2555201, 99588919, 102144120, 3981065479, 4083209599, 159143030241, 163226239840, 6361740144161, 6524966384001, 254310462736199, 260835429120200, 10166056769303799, 10426892198423999

Offset: 0

N. J. A. Sloane

The following remarks assume an offset of 1. This is the sequence of Lehmer numbers U_n(sqrt(R),Q) for the parameters R = 38 and Q = -1; it is a strong divisibility sequence, that is, gcd(a(n),a(m)) = a(gcd(n,m)) for all positive integers n and m. Consequently, this is a divisibility sequence: if n divides m then a(n) divides a(m). - Peter Bala, May 27 2014

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Eric W. Weisstein, MathWorld: Lehmer Number
Index entries for linear recurrences with constant coefficients, signature (0,40,0,-1).

Cf. A041758, A040379, A002530.

I:=[1,1,39,40]; [n le 4 select I[n] else 40*Self(n-2)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Dec 24 2013

Denominator[Convergents[Sqrt[399], 30]] (* Vincenzo Librandi, Dec 24 2013 *)

G.f.: -(x^2-x-1) / (x^4-40*x^2+1). - Colin Barker, Nov 24 2013
a(n) = 40*a(n-2) - a(n-4) for n > 3. - Vincenzo Librandi, Dec 24 2013
From Peter Bala, May 27 2014: (Start)
The following remarks assume an offset of 1.
Let alpha = ( sqrt(38) + sqrt(42) )/2 and beta = ( sqrt(38) - sqrt(42) )/2 be the roots of the equation x^2 - sqrt(38)*x - 1 = 0. Then a(n) = (alpha^n - beta^n)/(alpha - beta) for n odd, while a(n) = (alpha^n - beta^n)/(alpha^2 - beta^2) for n even.
a(n) = Product_{k = 1..floor((n-1)/2)} ( 38 + 4*cos^2(k*Pi/n) ).
Recurrence equations: a(0) = 0, a(1) = 1 and for n >= 1, a(2*n) = a(2*n - 1) + a(2*n - 2) and a(2*n + 1) = 38*a(2*n) + a(2*n - 1). (End)

More terms from Colin Barker, Nov 24 2013

A041839 Denominators of continued fraction convergents to sqrt(440).

Original entry on oeis.org

1, 1, 41, 42, 1721, 1763, 72241, 74004, 3032401, 3106405, 127288601, 130395006, 5343088841, 5473483847, 224282442721, 229755926568, 9414519505441, 9644275432009, 395185536785801, 404829812217810, 16588378025498201, 16993207837716011

Offset: 0

N. J. A. Sloane

The following remarks assume an offset of 1. This is the sequence of Lehmer numbers U_n(sqrt(R),Q) for the parameters R = 40 and Q = -1; it is a strong divisibility sequence, that is, gcd(a(n),a(m)) = a(gcd(n,m)) for all positive integers n and m. Consequently, this is a divisibility sequence: if n divides m then a(n) divides a(m). - Peter Bala, May 27 2014

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Eric W. Weisstein, MathWorld: Lehmer Number
Index entries for linear recurrences with constant coefficients, signature (0,42,0,-1).

Cf. A041838, A040419, A002530.

I:=[1,1,41,42]; [n le 4 select I[n] else 42*Self(n-2)-Self(n-4): n in [1..50]]; // Vincenzo Librandi, Dec 25 2013

Denominator[Convergents[Sqrt[440], 20]] (* Harvey P. Dale, Feb 21 2013 *)

G.f.: -(x^2-x-1) / (x^4-42*x^2+1). - Colin Barker, Nov 25 2013
a(n) = 42*a(n-2) - a(n-4) for n > 3. - Vincenzo Librandi, Dec 25 2013
From Peter Bala, May 27 2014: (Start)
The following remarks assume an offset of 1.
Let alpha = sqrt(10) + sqrt(11) and beta = sqrt(10) - sqrt(11) be the roots of the equation x^2 - sqrt(40)*x - 1 = 0. Then a(n) = (alpha^n - beta^n)/(alpha - beta) for n odd, while a(n) = (alpha^n - beta^n)/(alpha^2 - beta^2) for n even.
a(n) = Product_{k = 1..floor((n-1)/2)} ( 40 + 4*cos^2(k*Pi/n) ).
Recurrence equations: a(0) = 0, a(1) = 1 and for n >= 1, a(2*n) = a(2*n - 1) + a(2*n - 2) and a(2*n + 1) = 40*a(2*n) + a(2*n - 1). (End)

More terms from Colin Barker, Nov 25 2013

A041923 Denominators of continued fraction convergents to sqrt(483).

Original entry on oeis.org

1, 1, 43, 44, 1891, 1935, 83161, 85096, 3657193, 3742289, 160833331, 164575620, 7073009371, 7237584991, 311051578993, 318289163984, 13679196466321, 13997485630305, 601573592939131, 615571078569436, 26455558892855443, 27071129971424879

Offset: 0

N. J. A. Sloane

The following remarks assume an offset of 1. This is the sequence of Lehmer numbers U_n(sqrt(R),Q) for the parameters R = 42 and Q = -1; it is a strong divisibility sequence, that is, gcd(a(n),a(m)) = a(gcd(n,m)) for all positive integers n and m. Consequently, this is a divisibility sequence: if n divides m then a(n) divides a(m). - Peter Bala, May 27 2014

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Eric W. Weisstein, MathWorld: Lehmer Number
Index entries for linear recurrences with constant coefficients, signature (0,44,0,-1).

Cf. A041922, A176400, A040461, A002530.

I:=[1,1,43,44]; [n le 4 select I[n] else 44*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 27 2013

Denominator[Convergents[Sqrt[483], 30]] (* Vincenzo Librandi, Dec 27 2013 *)

G.f.: -(x^2 -x -1) / (x^4 -44*x^2 +1). - Colin Barker, Nov 27 2013
a(n) = 44*a(n-2) - a(n-4) for n > 3. - Vincenzo Librandi, Dec 27 2013
From Peter Bala, May 27 2014: (Start)
The following remarks assume an offset of 1.
Let alpha = ( sqrt(42) + sqrt(46) )/2 and beta = ( sqrt(42) - sqrt(46) )/2 be the roots of the equation x^2 - sqrt(42)*x - 1 = 0. Then a(n) = (alpha^n - beta^n)/(alpha - beta) for n odd, while a(n) = (alpha^n - beta^n)/(alpha^2 - beta^2) for n even.
a(n) = Product_{k = 1..floor((n-1)/2)} ( 42 + 4*cos^2(k*Pi/n) ).
Recurrence equations: a(0) = 0, a(1) = 1 and for n >= 1, a(2*n) = a(2*n - 1) + a(2*n - 2) and a(2*n + 1) = 42*a(2*n) + a(2*n - 1). (End)

More terms from Colin Barker, Nov 27 2013

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A041263 Denominators of continued fraction convergents to sqrt(143).

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A041311 Denominators of continued fraction convergents to sqrt(168).

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A041363 Denominators of continued fraction convergents to sqrt(195).

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A041419 Denominators of continued fraction convergents to sqrt(224).

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A041479 Denominators of continued fraction convergents to sqrt(255).

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A041543 Denominators of continued fraction convergents to sqrt(288).

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A041683 Denominators of continued fraction convergents to sqrt(360).

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