A010465 -id:A010465 - cp's OEIS frontend

A177925 Decimal expansion of sqrt(2730).

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

Offset: 2

Klaus Brockhaus, May 15 2010

Continued fraction expansion of sqrt(2730) is 52 followed by (repeat 4, 104).

sqrt(2730) = sqrt(2)*sqrt(3)*sqrt(5)*sqrt(7)*sqrt(13).

			sqrt(2730) = 52.24940191045252529379...

Cf. A002193 (decimal expansion of sqrt(2)), A002194 (decimal expansion of sqrt(3)), A002163 (decimal expansion of sqrt(5)), A010465 (decimal expansion of sqrt(7)), A010470 (decimal expansion of sqrt(13)), A177924 (decimal expansion of (28+sqrt(2730))/56).

RealDigits[Sqrt[2730],10,120][[1]] (* Harvey P. Dale, Aug 11 2021 *)

A022771 Ordered sequence of distinct terms of the form floor(x^i * floor(x^j)), i,j >= 0, where x = sqrt(7).

Original entry on oeis.org

1, 2, 5, 7, 14, 18, 37, 47, 49, 98, 126, 129, 259, 333, 341, 343, 686, 882, 903, 907, 1814, 2333, 2389, 2399, 2401, 4802, 6174, 6321, 6349, 6352, 12704, 16334, 16723, 16797, 16805, 16807, 33614, 43218, 44247, 44443, 44464, 44467, 88934

Offset: 1

Clark Kimberling

nonn

Cf. A010465 (sqrt(7)).

Offset corrected by Sean A. Irvine, May 21 2019

A114344 Starting position of the first n in the decimal expansion of the square root of n, or -1 if n never appears.

Original entry on oeis.org

1, 1, 5, 3, -1, 37, 39, 5, 2, -1, 89, 20, 52, 222, 319, 49, -1, 12, 99, 25, 144, 61, 41, 9, 109, -1, 145, 10, 268, 33, 189, 184, 155, 371, 45, 108, -1, 118, 26, 11, 149, 146, 108, 5, 235, 49, 299, 253, 32, -1, 103, 212, 120, 179, 353, 119, 225, 64, 10, 108, 104

Offset: 0

Cino Hilliard, Dec 22 2006, corrected Jul 18 2007

			For n=5, sqrt(5) = 2.23606797749978969640917366873127623544...
5 occurs in the 37th position so 37 is the 6th entry in the table counting from the 0th entry.

Cf. A002193, A002194, A002163, A010464, A010465, A010466, A010467.

digitpos(n) = { local(x,y,r,dot); for(x=0,n, r=sqrt(x); if(issquare(x), y=find(Str(floor(r)),x), y=find(Str(r),x); dot=find(Str(r),"."); if(dot < y, y--); ); if(y, print1(y","),print1(-1",") ) ) }
find(str,match) = /* Revised 2007 */ { local(lnm,lns,tstr,vstr,x,j); vstr=Vec(Str(str)); match=Str(match); lns=length(str); lnm=length(match); for(x=1,lns-lnm+1, tstr=""; for(j=x,x+lnm-1, tstr=concat(tstr,vstr[j]); ); if(match==tstr,return(x)) ); return(0); }

A161368 Engel expansion of sqrt(7).

Original entry on oeis.org

1, 1, 2, 4, 7, 7, 8, 14, 16, 21, 36, 40, 41, 354, 407, 568, 2253, 2392, 6783, 8608, 10968, 23813, 149663, 1353193, 2273258, 11992211, 18888350, 35589752, 279408946, 926928928, 7122445646, 12200380022, 24793374441, 1006675801235

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jun 08 2009

nonn

			2.645751311... = 1/1+1/(1*1)+1/(1*1*2)+1/(1*1*2*4)+1/(1*1*2*4*7)+1/(1*1*2*4*7*7)+....

Index to sequences related to Engel expansions

Cf. A010465, A059176.

EngelExp[A_,n_]:=Join[Array[1&,Floor[A]],First@Transpose@NestList[ {Ceiling[1/Expand[ #[[1]]#[[2]]-1]], Expand[ #[[1]]#[[2]]-1]}&, {Ceiling[1/(A-Floor[A])], A-Floor[A]}, n-1]]; EngelExp[N[7^(1/2),7! ],50]

Added example and link to index - R. J. Mathar, Sep 23 2009

A171536 Decimal expansion of 2/sqrt(7).

Original entry on oeis.org

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

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 -5/2>.

			sqrt(4/7) = 0.75592894601845445442903307...

Wikipedia, Table of Clebsch-Gordan coefficients

RealDigits[2/Sqrt[7],10,120][[1]] (* Harvey P. Dale, Jan 02 2022 *)

equals 2*A020764 = 2/A010465.

cp's OEIS Frontend

A177925 Decimal expansion of sqrt(2730).

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A022771 Ordered sequence of distinct terms of the form floor(x^i * floor(x^j)), i,j >= 0, where x = sqrt(7).

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A114344 Starting position of the first n in the decimal expansion of the square root of n, or -1 if n never appears.

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A161368 Engel expansion of sqrt(7).

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A171536 Decimal expansion of 2/sqrt(7).

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