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A010490 Decimal expansion of square root of 35. 18
5, 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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Continued fraction expansion is 5 followed by {1, 10} repeated. - Harry J. Smith, Jun 04 2009

A010490^2 = 35 is the only integer > 0 of form n(n+2), one less than a square, that is also of form n(n+1)(n+2)/6, a tetrahedral number (true for n = 5). Consequence of this, sqrt (35) is the only n in R > 0 such that the following equivalency holds (for n = 5): Where Spin(n/2) = h/(4*Pi)sqrt(n(n+2)) and h = Planck's Constant (A003676), then I. 4*Pi/h*Spin(n/2) = II. The square root of the sum of the relative intensities of the transition states of a Spin(n/2) particle (relative to spin 1/2). Regarding II., for clarification see comments dated May 26 2012 by Stanislav Sykora in A003991. - Raphie Frank, Dec 19 2012

This sequence is associated with Sophie Germain triangular numbers of the first and second kinds, as defined in A217278, by the formula sqrt 35 = sqrt ((A217278(n) - A217278(n-12))/(A217278(n-4) - A217278(n-8))). - Raphie Frank, Dec 22 2012

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..20000

Wikipedia, Spin (Physics)

EXAMPLE

5.916079783099616042567328291561617048415501230794340322879719669142822...

MATHEMATICA

RealDigits[N[Sqrt[35], 105]][[1]] (* Vladimir Joseph Stephan Orlovsky, Feb 20 2011 *)

PROG

(PARI) { default(realprecision, 20080); x=sqrt(35); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010490.txt", n, " ", d)); } \\ Harry J. Smith, Jun 04 2009

CROSSREFS

Cf. A040029 (continued fraction).

Sequence in context: A186192 A231532 A086201 * A021173 A266553 A063921

Adjacent sequences:  A010487 A010488 A010489 * A010491 A010492 A010493

KEYWORD

nonn,cons

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified January 17 14:12 EST 2019. Contains 319225 sequences. (Running on oeis4.)