A010168 -id:A010168 - cp's OEIS frontend

A010548 Decimal expansion of square root of 97.

9, 8, 4, 8, 8, 5, 7, 8, 0, 1, 7, 9, 6, 1, 0, 4, 7, 2, 1, 7, 4, 6, 2, 1, 1, 4, 1, 4, 9, 1, 7, 6, 2, 4, 4, 8, 1, 6, 9, 6, 1, 3, 6, 2, 8, 7, 4, 4, 2, 7, 6, 4, 1, 7, 1, 7, 2, 3, 1, 5, 4, 5, 2, 9, 8, 3, 6, 4, 4, 0, 5, 8, 3, 7, 0, 7, 6, 7, 8, 6, 3, 0, 0, 9, 3, 2, 0, 0, 7, 8, 4, 1, 1, 5, 4, 2, 5, 7, 6

Offset: 1

N. J. A. Sloane

Continued fraction expansion is 9 followed by {1, 5, 1, 1, 1, 1, 1, 1, 5, 1, 18} repeated. - Harry J. Smith, Jun 12 2009

			9.848857801796104721746211414917624481696136287442764171723154529836440...

Harry J. Smith, Table of n, a(n) for n = 1..20000
Index entries for algebraic numbers, degree 2.

Cf. A010168 Continued fraction.

RealDigits[N[97^(1/2),200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Jan 24 2012 *)

{ default(realprecision, 20080); x=sqrt(97); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010548.txt", n, " ", d)); } \\ Harry J. Smith, Jun 12 2009

A041174 Numerators of continued fraction convergents to sqrt(97).

Original entry on oeis.org

9, 10, 59, 69, 128, 197, 325, 522, 847, 4757, 5604, 105629, 111233, 661794, 773027, 1434821, 2207848, 3642669, 5850517, 9493186, 53316447, 62809633, 1183889841, 1246699474, 7417387211, 8664086685, 16081473896, 24745560581, 40827034477, 65572595058

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,11208,0,0,0,0,0,0,0,0,0,0,1).

Cf. A010548, A041175, A010168, A020854.

Numerator[Convergents[Sqrt[97], 30]] (* Vincenzo Librandi, Oct 30 2013 *)
LinearRecurrence[{0,0,0,0,0,0,0,0,0,0,11208,0,0,0,0,0,0,0,0,0,0,1},{9,10,59,69,128,197,325,522,847,4757,5604,105629,111233,661794,773027,1434821,2207848,3642669,5850517,9493186,53316447,62809633},30] (* Harvey P. Dale, Aug 02 2021 *)

G.f.: -(x^21 -9*x^20 +10*x^19 -59*x^18 +69*x^17 -128*x^16 +197*x^15 -325*x^14 +522*x^13 -847*x^12 +4757*x^11 +5604*x^10 +4757*x^9 +847*x^8 +522*x^7 +325*x^6 +197*x^5 +128*x^4 +69*x^3 +59*x^2 +10*x +9) / (x^22 +11208*x^11 -1). - Colin Barker, Nov 14 2013

More terms from Colin Barker, Nov 14 2013

A041175 Denominators of continued fraction convergents to sqrt(97).

Original entry on oeis.org

1, 1, 6, 7, 13, 20, 33, 53, 86, 483, 569, 10725, 11294, 67195, 78489, 145684, 224173, 369857, 594030, 963887, 5413465, 6377352, 120205801, 126583153, 753121566, 879704719, 1632826285, 2512531004, 4145357289, 6657888293, 10803245582, 60674116203, 71477361785

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,11208,0,0,0,0,0,0,0,0,0,0,1).

Cf. A041174, A010168, A020854, A010548.

I:=[1, 1, 6, 7, 13, 20, 33, 53, 86, 483, 569, 10725, 11294, 67195, 78489, 145684, 224173, 369857, 594030, 963887, 5413465, 6377352]; [n le 22 select I[n] else 11208*Self(n-11)+Self(n-22): n in [1..40]]; // Vincenzo Librandi, Dec 12 2013

Denominator[Convergents[Sqrt[97], 30]] (* Vincenzo Librandi, Dec 12 2013 *)

G.f.: -(x^20 -x^19 +6*x^18 -7*x^17 +13*x^16 -20*x^15 +33*x^14 -53*x^13 +86*x^12 -483*x^11 +569*x^10 +483*x^9 +86*x^8 +53*x^7 +33*x^6 +20*x^5 +13*x^4 +7*x^3 +6*x^2 +x +1) / (x^22 +11208*x^11 -1). - Colin Barker, Nov 14 2013

a(n) = 11208*a(n-11) + a(n-22). - Vincenzo Librandi, Dec 12 2013

More terms from Colin Barker, Nov 14 2013

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A010548 Decimal expansion of square root of 97.

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A041174 Numerators of continued fraction convergents to sqrt(97).

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A041175 Denominators of continued fraction convergents to sqrt(97).

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Magma

Mathematica

Formula

Extensions