A142238 -id:A142238 - cp's OEIS frontend

A382713 Simple continued fraction expansion of sqrt(3/2).

1, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2

Offset: 0

N. J. A. Sloane, Apr 08 2025

Index entries for linear recurrences with constant coefficients, signature (0,1).

Cf. A105397, A115754, A142238, A142239.

Essentially the same as A106469, A040003, A010694.

with(numtheory); cfrac (sqrt(3/2, 70, 'quotients');

PadRight[{1}, 100, {2, 4}] (* Paolo Xausa, Apr 14 2025 *)

def A382713(n): return 1<<1+(n&1) if n else 1 # Chai Wah Wu, Apr 09 2025

A379919 Numbers k that are the maximum of integers |k2|, |k3|, |k5| with |k2| + |k3| + |k5| > 0, and |k2sqrt(2) + k3sqrt(3) + k5*sqrt(5)| is smaller than for any smaller value of k.

Original entry on oeis.org

1, 2, 4, 5, 10, 27, 94, 151, 245, 296, 349, 396, 435, 1835, 10235, 18708, 31637, 53519, 160958, 535529, 643427

Offset: 1

Hugo Pfoertner, Jan 07 2025

Maximum absolute value of coefficients in a linear combination of square roots of the first 3 primes producing a new best approximation of 0.

a(22) > 10^6.

			Signs of k2, k3, k5 chosen to get sum > 0.
   n  a(n)  *sqrt(2) *sqrt(3) *sqrt(5)        sum
   1     1        -1        1        0   3.1783724520E-1
   2     2         2        1       -2   8.8341977315E-2
   3     4        -4        2        1   4.3315343145E-2
   4     5        -3       -4        5   9.4959701042E-3
   5    10        10       -3       -4   1.7112910252E-3
   6    27       -22       27       -7   1.9758965307E-4
   7    94        94        2      -61   2.9850721518E-5
   8   151      -151      122        1   1.8582565467E-5
   9   245       245     -120      -62   1.1268156051E-5
  10   296      -190     -227      296   1.1170914545E-5
  11   349        39      349     -295   7.4116509219E-6
  12   396      -396      242       63   7.3144094166E-6
  13   435       435      107     -358   9.7241505322E-8
  14  1835      -932    -1608     1835   9.6348194355E-9

Cf. A142238.

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A382713 Simple continued fraction expansion of sqrt(3/2).

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A379919 Numbers k that are the maximum of integers |k2|, |k3|, |k5| with |k2| + |k3| + |k5| > 0, and |k2sqrt(2) + k3sqrt(3) + k5*sqrt(5)| is smaller than for any smaller value of k.

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cp's OEIS Frontend

A382713 Simple continued fraction expansion of sqrt(3/2).

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Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

Python

A379919 Numbers k that are the maximum of integers |k2|, |k3|, |k5| with |k2| + |k3| + |k5| > 0, and |k2*sqrt(2) + k3*sqrt(3) + k5*sqrt(5)| is smaller than for any smaller value of k.

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A379919 Numbers k that are the maximum of integers |k2|, |k3|, |k5| with |k2| + |k3| + |k5| > 0, and |k2sqrt(2) + k3sqrt(3) + k5*sqrt(5)| is smaller than for any smaller value of k.