Doodson numbers

Remarks

Example: the principal lunar semidiurnal tide $M_2$ has argument $2\tau$, so $(k_1, \dots, k_6) = (2, 0, 0, 0, 0, 0)$ and its Doodson number is $255.555$. Since solar time is $\tau + s - h$, the solar semidiurnal tide $S_2$ has argument $2\tau + 2s - 2h$ and number $273.555$. The diurnal tides $K_1$ and $O_1$ have arguments $\tau + s$ and $\tau - s$, and numbers $165.555$ and $145.555$. The first digit $k_1$ is the species: $0$ long period, $1$ diurnal, $2$ semidiurnal, $3$ terdiurnal. Non-example: the list $(2, 0, 0, 0, 0, 0)$ written without the shift, as $200.000$, is not the Doodson number of $M_2$. The shift by $5$ in the last five places is part of the code. The fortnightly constituent $MS_f$, with argument $2s - 2h$, has number $073.555$.