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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.

%I A379919 #19 Jan 10 2025 02:04:00
%S A379919 1,2,4,5,10,27,94,151,245,296,349,396,435,1835,10235,18708,31637,
%T A379919 53519,160958,535529,643427
%N 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.
%C A379919 Maximum absolute value of coefficients in a linear combination of square roots of the first 3 primes producing a new best approximation of 0.
%C A379919 a(22) > 10^6.
%e A379919 Signs of k2, k3, k5 chosen to get sum > 0.
%e A379919    n  a(n)  *sqrt(2) *sqrt(3) *sqrt(5)        sum
%e A379919    1     1        -1        1        0   3.1783724520E-1
%e A379919    2     2         2        1       -2   8.8341977315E-2
%e A379919    3     4        -4        2        1   4.3315343145E-2
%e A379919    4     5        -3       -4        5   9.4959701042E-3
%e A379919    5    10        10       -3       -4   1.7112910252E-3
%e A379919    6    27       -22       27       -7   1.9758965307E-4
%e A379919    7    94        94        2      -61   2.9850721518E-5
%e A379919    8   151      -151      122        1   1.8582565467E-5
%e A379919    9   245       245     -120      -62   1.1268156051E-5
%e A379919   10   296      -190     -227      296   1.1170914545E-5
%e A379919   11   349        39      349     -295   7.4116509219E-6
%e A379919   12   396      -396      242       63   7.3144094166E-6
%e A379919   13   435       435      107     -358   9.7241505322E-8
%e A379919   14  1835      -932    -1608     1835   9.6348194355E-9
%Y A379919 Cf. A142238.
%K A379919 nonn,more
%O A379919 1,2
%A A379919 _Hugo Pfoertner_, Jan 07 2025