A379918 Numbers k that are the maximum of integers |k3|, |k5|, |k7| with |k3| + |k5| + |k7| > 0, and |k3*sqrt(3) + k5*sqrt(5) + k7*sqrt(7)| is smaller than for any smaller value of k.

1, 2, 3, 23, 48, 71, 1766, 1837, 2387, 3103, 3152, 10963, 26353, 53533, 101626, 122825, 258586, 331933, 590519, 920650

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..20.

Hugo Pfoertner, Fortran program, (2025).

Example

   n    a(n)       abs(sum)        *sqrt(3)    *sqrt(5)    *sqrt(7)
   1       1   4.0968333356E-01           0           1          -1
   2       2   9.4333836366E-02          -1           2          -1
   3       3   1.0163630564E-03          -2          -2           3
   4      23   3.3896123436E-04         -19          23          -7
   5      48   3.3844058772E-04         -36          48         -17
   6      71   5.2064664313E-07         -55          71         -24
   7    1766   3.2330415667E-07       -1148        1766        -741
   8    1837   1.9734248646E-07       -1203        1837        -765
   9    2387   1.8929812839E-07       -1955       -1310        2387
  10    3103   1.3400602829E-07        3103        -456       -1646
  11    3152   8.0443580712E-09        -752       -3147        3152
  12   10963   7.1124612174E-10       10963       -8189        -256
  13   26353   3.0716027901E-10      -21285      -14694       26353
  14   53533   9.6925563716E-11       53533       21199      -52962
  15  101626   8.6509546965E-11     -100060      101626      -20385
  16  122825   1.0416016751E-11      -46527      122825      -73347
  17  258586   5.9675711147E-12     -135357     -201116      258586
  18  331933   4.4484456360E-12      -88830     -323941      331933
  19  590519   1.5191254787E-12     -224187     -525057      590519
  20  920650   1.4316200173E-13      920650      -34112     -573877

Prog

(Fortran) C See link.

Crossrefs

Cf. A379919.

Sequence in context: A262838 A120366 A371310 * A041787 A143853 A195241

Adjacent sequences: A379915 A379916 A379917 * A379919 A379920 A379921

Keyword

nonn,more

Author

Hugo Pfoertner, Jan 10 2025

Status

approved