A178832 Number of minima of the 1-D Griewank function in [-n, n].

1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 9, 9, 9, 9, 9, 9, 11, 11, 11, 11, 11, 11, 13, 13, 13, 13, 13, 13, 15, 15, 15, 15, 15, 15, 15, 17, 17, 17, 17, 17, 17, 19, 19, 19, 19, 19, 19, 21, 21, 21, 21, 21, 21, 21, 23, 23, 23, 23, 23, 23, 25, 25, 25, 25, 25, 25, 27, 27, 27, 27, 27, 27, 29, 29, 29, 29, 29, 29, 29, 31, 31, 31, 31, 31, 31, 33, 33, 33, 33, 33, 33, 35, 35

Offset

0,8

Comments

Appears to be equal to the number of positive roots for x-cos(nx)=0. - Yuriy Sibirmovsky, Sep 11 2016

Links

Table of n, a(n) for n=0..108.

Eric Weisstein's World of Mathematics, Griewank Function

Example

Minima occur at 0 and near +/- 6.28005, 12.5601, 18.8401, 25.1202, ...

Mathematica

A = Table[{n, CountRoots[x - Cos[n x], {x, 0, Infinity}]}, {n, 0, 108}]; (* (!) Conjecture, may not be correct for larger n (!) Yuriy Sibirmovsky, Sep 11 2016 *)

Crossrefs

Cf. A177889.

Sequence in context: A362049 A333819 A216944 * A111233 A210746 A283986

Adjacent sequences: A178829 A178830 A178831 * A178833 A178834 A178835

Keyword

nonn

Author

Eric W. Weisstein, Dec 27 2010

Status

approved