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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.

%I A379918 #8 Jan 12 2025 07:57:01
%S A379918 1,2,3,23,48,71,1766,1837,2387,3103,3152,10963,26353,53533,101626,
%T A379918 122825,258586,331933,590519,920650
%N 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.
%C A379918 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.
%H A379918 Hugo Pfoertner, <a href="/A379918/a379918.txt">Fortran program</a>, (2025).
%e A379918    n    a(n)       abs(sum)        *sqrt(3)    *sqrt(5)    *sqrt(7)
%e A379918    1       1   4.0968333356E-01           0           1          -1
%e A379918    2       2   9.4333836366E-02          -1           2          -1
%e A379918    3       3   1.0163630564E-03          -2          -2           3
%e A379918    4      23   3.3896123436E-04         -19          23          -7
%e A379918    5      48   3.3844058772E-04         -36          48         -17
%e A379918    6      71   5.2064664313E-07         -55          71         -24
%e A379918    7    1766   3.2330415667E-07       -1148        1766        -741
%e A379918    8    1837   1.9734248646E-07       -1203        1837        -765
%e A379918    9    2387   1.8929812839E-07       -1955       -1310        2387
%e A379918   10    3103   1.3400602829E-07        3103        -456       -1646
%e A379918   11    3152   8.0443580712E-09        -752       -3147        3152
%e A379918   12   10963   7.1124612174E-10       10963       -8189        -256
%e A379918   13   26353   3.0716027901E-10      -21285      -14694       26353
%e A379918   14   53533   9.6925563716E-11       53533       21199      -52962
%e A379918   15  101626   8.6509546965E-11     -100060      101626      -20385
%e A379918   16  122825   1.0416016751E-11      -46527      122825      -73347
%e A379918   17  258586   5.9675711147E-12     -135357     -201116      258586
%e A379918   18  331933   4.4484456360E-12      -88830     -323941      331933
%e A379918   19  590519   1.5191254787E-12     -224187     -525057      590519
%e A379918   20  920650   1.4316200173E-13      920650      -34112     -573877
%o A379918 (Fortran) C See link.
%Y A379918 Cf. A379919.
%K A379918 nonn,more
%O A379918 1,2
%A A379918 _Hugo Pfoertner_, Jan 10 2025