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.

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

Offset

1,2

Comments

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.

Links

Table of n, a(n) for n=1..21.

Example

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

Crossrefs

Cf. A142238.

Sequence in context: A110789 A125952 A337661 * A248127 A258253 A177244

Adjacent sequences: A379916 A379917 A379918 * A379920 A379921 A379922

Keyword

nonn,more

Author

Hugo Pfoertner, Jan 07 2025

Status

approved