A005483 -id:A005483 - cp's OEIS frontend

A005482 Decimal expansion of cube root of 7.

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

Offset: 1

N. J. A. Sloane

			1.9129311827723891011991168...

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Harry J. Smith, Table of n, a(n) for n = 1..20000
Index entries for algebraic numbers, degree 3.

Cf. A005483 (continued fraction). - Harry J. Smith, May 07 2009

RealDigits[N[7^(1/3), 200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Jan 22 2012 *)

{ default(realprecision, 20080); x=7^(1/3); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b005482.txt", n, " ", d)); } \\ Harry J. Smith, May 07 2009, corrected May 19 2009

More terms from Olaf Voß, Feb 13 2008

A182630 T(n,k) = A002024(k+1)*n + A002262(k), n >= 0, k >= 0, read by antidiagonals.

Original entry on oeis.org

0, 1, 0, 2, 2, 1, 3, 4, 3, 0, 4, 6, 5, 3, 1, 5, 8, 7, 6, 4, 2, 6, 10, 9, 9, 7, 5, 0, 7, 12, 11, 12, 10, 8, 4, 1, 8, 14, 13, 15, 13, 11, 8, 5, 2, 9, 16, 15, 18, 16, 14, 12, 9, 6, 3, 10, 18, 17, 21, 19, 17, 16, 13, 10, 7, 0

Offset: 0

Omar E. Pol, Dec 06 2010

A table of congruences.

See A182631 for another version.

			Table of congruences:
===============+====+=======+==========+=============+====
           mod |  1 |   2   |     3    |      4      | ...
===============+====+=======+==========+=============+====
  congruent to |  0 |  0  1 |  0  1  2 |  0  1  2  3 | ...
===============+====+=======+==========+=============+====
Array begins:  |  0 |  0  1 |  0  1  2 |  0  1  2  3 | ...
               |  1 |  2  3 |  3  4  5 |  4  5  6  7 | ...
               |  2 |  4  5 |  6  7  8 |  8  9 10 11 | ...
               |  3 |  6  7 |  9 10 11 | 12 13 14 15 | ...
               |  4 |  8  9 | 12 13 14 | 16 17 18 19 | ...
               |  5 | 10 11 | 15 16 17 | 20 21 22 23 | ...
               |  6 | 12 13 | 18 19 20 | 24 25 26 27 | ...
               |  7 | 14 15 | 21 22 23 | 28 29 30 31 | ...
               |  8 | 16 17 | 24 25 26 | 32 33 34 35 | ...
               |  9 | 18 19 | 27 28 29 | 36 37 38 39 | ...
               | 10 | 20 21 | 30 31 32 | 40 41 42 43 | ...

Columns: A001477, A005483, A005408, A008585, A016777, A016789, A008586, A016813, A016825, A004767.
Rows: A002262, A094727, A182815.
Cf. A182631.

A002262 := proc(n) n-binomial(floor(1/2+sqrt(2+2*n)),2) ; end proc:
A002024 := proc(n) ceil((sqrt(1+8*n)-1)/2) ;end proc:
A182630 := proc(n,k) A002024(k+1)*n+A002262(k) ; end proc: # R. J. Mathar, Dec 09 2010

A005484 Numerators of continued fraction convergents to cube root of 7.

Original entry on oeis.org

1, 2, 21, 44, 725, 1494, 2219, 10370, 22959, 33329, 722868, 756197, 2991459, 15713492, 18704951, 53123394, 71828345, 124951739, 321731823, 3664001792, 18641740783, 22305742575, 85558968508, 107864711083, 301288390674, 8242651259281, 33271893427798, 41514544687079

Offset: 0

N. J. A. Sloane, Herman P. Robinson

D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 105, National Research Council, Washington, DC, 1941, p. 67.
P. Seeling, Verwandlung der irrationalen Groesse ... in einen Kettenbruch, Archiv. Math. Phys., 46 (1866), 80-120.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Vincenzo Librandi, Table of n, a(n) for n = 0..999

Cf. A005482, A005483, A005485 (denominators).

Numerator[Convergents[7^(1/3), 40]] (* Vincenzo Librandi, Sep 08 2013 *)

a(n)= contfracpnqn(contfrac(7^(1/3), n))[1, 1]; \\ Michel Marcus, Sep 07 2013

More terms from Michel Marcus, Sep 07 2013
Inserted a(27) by Vincenzo Librandi, Sep 08 2013
Offset changed by Andrew Howroyd, Jul 05 2024

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A005482 Decimal expansion of cube root of 7.

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A182630 T(n,k) = A002024(k+1)*n + A002262(k), n >= 0, k >= 0, read by antidiagonals.

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A005484 Numerators of continued fraction convergents to cube root of 7.

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