A010490 -id:A010490 - cp's OEIS frontend

A196737 Decimal expansion of (4*Pi^2)/sqrt(35) = A212002/A010490.

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

Offset: 1

Raphie Frank, Dec 21 2012

This sequence is exactly equal to (Pi*h)/Spin(5/2), where h = Planck's Constant = A003676 and Spin(n/2) = h/(4*Pi) * sqrt(n(n+2)) = A003676/(10*A019694) * sqrt(A005563(n)).

			6.673070521654371272396016391388419924371668300691857264579256516590541...

Wikipedia, Spin (physics)

Cf. A212002, A010490.

RealDigits[(4Pi^2)/Sqrt[35],10,120][[1]] (* Harvey P. Dale, Jan 26 2021 *)

A248262 Egyptian fraction representation of sqrt(35) (A010490) using a greedy function.

Original entry on oeis.org

5, 2, 3, 13, 172, 106165, 18285649425, 2186743227575352844102, 34485253453894276212351220254887863775700566, 1196120890861075329034546890130985440938005448458845105688952404014155813652248242764257

Offset: 0

Robert G. Wilson v, Oct 04 2014

nonn

Egyptian fraction representations of the square roots: A006487, A224231, A248235-A248322.

Egyptian fraction representations of the cube roots: A129702, A132480-A132574.

Egyptian[nbr_] := Block[{lst = {IntegerPart[nbr]}, cons = N[ FractionalPart[ nbr], 2^20], denom, iter = 8}, While[ iter > 0, denom = Ceiling[ 1/cons]; AppendTo[ lst, denom]; cons -= 1/denom; iter--]; lst]; Egyptian[ Sqrt[ 35]]

A090656 Decimal expansion of 5 + sqrt(35).

Original entry on oeis.org

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

Offset: 2

Felix Tubiana, Feb 05 2004

Equals n+n/(n+n/(n+n/(n+....))) for n = 10. See also A090388. - Stanislav Sykora, Jan 23 2014

			10.9160797830996160...

Chai Wah Wu, Table of n, a(n) for n = 2..10003
Index entries for algebraic numbers, degree 2

Equals A010490 plus 5. - R. J. Mathar, Sep 08 2008
Cf. A161321.
Cf. n+n/(n+n/(n+...)): A090388 (n=2), A090458 (n=3), A090488 (n=4), A090550 (n=5), A092294 (n=6), A092290 (n=7), A090654 (n=8), A090655 (n=9). - Stanislav Sykora, Jan 23 2014

RealDigits[5+Sqrt[35],10,120][[1]] (* Harvey P. Dale, Jun 17 2014 *)

sqrt(35)+5 \\ Charles R Greathouse IV, Apr 25 2016

A041059 Denominators of continued fraction convergents to sqrt(35).

Original entry on oeis.org

1, 1, 11, 12, 131, 143, 1561, 1704, 18601, 20305, 221651, 241956, 2641211, 2883167, 31472881, 34356048, 375033361, 409389409, 4468927451, 4878316860, 53252096051, 58130412911, 634556225161, 692686638072, 7561422605881, 8254109243953, 90102515045411

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 = 10 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 Weisstein's World of Mathematics, Lehmer Number
Index entries for linear recurrences with constant coefficients, signature (0,12,0,-1).

Cf. A010490, A041058, A002539.

Denominator[Convergents[Sqrt[35], 30]] (* Vincenzo Librandi, Oct 23 2013 *)

G.f.: (1+x-x^2)/(1-12*x^2+x^4). - Colin Barker, Jan 01 2012
From Peter Bala, May 28 2014: (Start)
The following remarks assume an offset of 1.
Let alpha = ( sqrt(10) + sqrt(14) )/2 and beta = ( sqrt(10) - sqrt(14) )/2 be the roots of the equation x^2 - sqrt(10)*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)} ( 10 + 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) = 10*a(2*n) + a(2*n - 1). (End)

A040029 Continued fraction for sqrt(35).

Original entry on oeis.org

5, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1

Offset: 0

N. J. A. Sloane

			5.9160797830996160425673282... = 5 + 1/(1 + 1/(10 + 1/(1 + 1/(10 + ...)))). - _Harry J. Smith_, Jun 04 2009

James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, pages 275-276.

Harry J. Smith, Table of n, a(n) for n = 0..20000
G. Xiao, Contfrac.
Index entries for continued fractions for constants.
Index entries for linear recurrences with constant coefficients, signature (0,1).

Cf. A010490 (decimal expansion), A010691.

Digits := 100: convert(evalf(sqrt(N)),confrac,90,'cvgts'):

ContinuedFraction[Sqrt[35],300] (* Vladimir Joseph Stephan Orlovsky, Mar 06 2011 *)
PadRight[{5},120,{10,1}] (* Harvey P. Dale, Mar 23 2021 *)

{ allocatemem(932245000); default(realprecision, 22000); x=contfrac(sqrt(35)); for (n=0, 20000, write("b040029.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 04 2009

From Amiram Eldar, Nov 12 2023: (Start)
Multiplicative with a(2^e) = 10, and a(p^e) = 1 for an odd prime p.
Dirichlet g.f.: zeta(s) * (1 + 9/2^s). (End)
G.f.: (5 + x + 5*x^2)/(1 - x^2). - Stefano Spezia, Jul 27 2025

A171543 Decimal expansion of 2/sqrt(35).

Original entry on oeis.org

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

Offset: 0

R. J. Mathar, Dec 11 2009

The absolute value of the Clebsch-Gordan coupling coefficient = <2 3/2 ; -1 3/2 | 7/2 1/2>.

			sqrt(4/35) = 2/sqrt(35) = 0.33806170189140663100384733094637811705...

Daniel Starodubtsev, Table of n, a(n) for n = 0..10000
Wikipedia, Table of Clebsch-Gordan coefficients

Cf. A010490, A171538.

RealDigits[2/Sqrt[35],10,120][[1]] (* Harvey P. Dale, Aug 23 2014 *)

2/sqrt(35) \\ Michel Marcus, Feb 18 2020

Equals 2/A010490 = A171538/2.

A010606 Decimal expansion of cube root of 35.

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 1..5000

Cf. A010490 (sqrt(35)).

Cf. A010604, A010605, A010607.

RealDigits[N[35^(1/3),200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Feb 15 2012 *)

sqrtn(35,3) \\ Charles R Greathouse IV, Apr 14 2014

A041058 Numerators of continued fraction convergents to sqrt(35).

Original entry on oeis.org

5, 6, 65, 71, 775, 846, 9235, 10081, 110045, 120126, 1311305, 1431431, 15625615, 17057046, 186196075, 203253121, 2218727285, 2421980406, 26438531345, 28860511751, 315043648855, 343904160606, 3754085254915

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 (0,12,0,-1).

Cf. A010490, A041059.

Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[35], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 21 2011 *)
Numerator[Convergents[Sqrt[35], 30]] (* Vincenzo Librandi, Oct 23 2013 *)

a(n) = 12*a(n-2)-a(n-4). G.f.: (5+6*x+5*x^2-x^3)/(1-12*x^2+x^4). [Colin Barker, Apr 17 2012]

A161321 Decimal expansion of (sqrt(35)-5)/10.

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane, Nov 22 2009

			.091607978309961604256732829156161704841550123079434032287971...

D. Mumford et al., Indra's Pearls, Cambridge 2002; see p. 321.

Daniel Starodubtsev, Table of n, a(n) for n = 0..10000

Cf. A090656, A010490.

(sqrt(35)-5)/10 \\ Michel Marcus, Feb 16 2020

A171538 Decimal expansion of 4/sqrt(35).

Original entry on oeis.org

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

Offset: 0

R. J. Mathar, Dec 11 2009

The absolute value of the Clebsch-Gordan coupling coefficient = <2 3/2 ; -2 1/2 | 5/2 -3/2>.

			sqrt(16/35) = 0.67612340378281326200769466...

Daniel Starodubtsev, Table of n, a(n) for n = 0..10000
Wikipedia, Table of Clebsch-Gordan coefficients

RealDigits[4/Sqrt[35],10,120][[1]] (* Harvey P. Dale, Mar 29 2018 *)

equals 4/A010490 = 2*A171543 .

cp's OEIS Frontend

A196737 Decimal expansion of (4*Pi^2)/sqrt(35) = A212002/A010490.

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A248262 Egyptian fraction representation of sqrt(35) (A010490) using a greedy function.

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A090656 Decimal expansion of 5 + sqrt(35).

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A041059 Denominators of continued fraction convergents to sqrt(35).

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A040029 Continued fraction for sqrt(35).

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A171543 Decimal expansion of 2/sqrt(35).

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A010606 Decimal expansion of cube root of 35.

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A041058 Numerators of continued fraction convergents to sqrt(35).

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