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

Author

Hugo Pfoertner, Jan 07 2025

Keywords

• nonn
• more

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.

Examples

			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.