A379919 - OEIS

%I #19 Jan 10 2025 02:04:00

%S 1,2,4,5,10,27,94,151,245,296,349,396,435,1835,10235,18708,31637,

%T 53519,160958,535529,643427

%N 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 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 a(22) > 10^6.

%e Signs of k2, k3, k5 chosen to get sum > 0.

%e    n  a(n)  *sqrt(2) *sqrt(3) *sqrt(5)        sum

%e    1     1        -1        1        0   3.1783724520E-1

%e    2     2         2        1       -2   8.8341977315E-2

%e    3     4        -4        2        1   4.3315343145E-2

%e    4     5        -3       -4        5   9.4959701042E-3

%e    5    10        10       -3       -4   1.7112910252E-3

%e    6    27       -22       27       -7   1.9758965307E-4

%e    7    94        94        2      -61   2.9850721518E-5

%e    8   151      -151      122        1   1.8582565467E-5

%e    9   245       245     -120      -62   1.1268156051E-5

%e   10   296      -190     -227      296   1.1170914545E-5

%e   11   349        39      349     -295   7.4116509219E-6

%e   12   396      -396      242       63   7.3144094166E-6

%e   13   435       435      107     -358   9.7241505322E-8

%e   14  1835      -932    -1608     1835   9.6348194355E-9

%Y Cf. A142238.

%K nonn,more

%O 1,2

%A _Hugo Pfoertner_, Jan 07 2025