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Descoperiti regula si completati sirul cu urmatorul element.

1
11
21
1112
3112
211213
312213

Draguta problema, insa cred ca e mai potrivita pentru sectiunea de matematica distractiva .

Exista o corespondenta intre numerele de pe linia \( k+1 \) si linia \( k \) , asa cum am aratat am jos ...

\( \begin{array}{cccccccccccc}
1 \\\\\\\\
1\ \overline{\underline{\left| 1\right|}} & \mbox{pe linia 1 se afla \underline{un} 1}\\\\\\\\
2\ \overline{\underline{\left| 1\right|}} & \mbox{ pe linia 2 se afla \underline{doi} de 1}\\\\\\\\
1\ \overline{\underline{\left| 1\right|}}\ \ 1\ \overline{\underline{\left| 2\right|}} & \mbox{ pe linia 3 se afla \underline{un} 1 si \underline{un} 2} \\\\\\\\
3\ \overline{\underline{\left| 1\right|}}\ \ 1\ \overline{\underline{\left| 2\right|}} & \mbox{ pe linia 4 se afla \underline{trei} de 1 si \underline{un} 2} \\\\\\\\
2\ \overline{\underline{\left| 1\right|}}\ \ 1\ \overline{\underline{\left| 2\right|}}\ \ 1\ \overline{\underline{\left| 3\right|}} & \vdots \\\\\\\\
3\ \overline{\underline{\left| 1\right|}}\ \ 2\ \overline{\underline{\left| 2\right|}}\ \ 1\ \overline{\underline{\left| 3\right|}} \\\\\\\\
2\ \overline{\underline{\left| 1\right|}}\ \ 2\ \overline{\underline{\left| 2\right|}}\ \ 2\ \overline{\underline{\left| 3\right|}} \\\\\\\\
1\ \overline{\underline{\left| 1\right|}}\ \ 4\ \overline{\underline{\left| 2\right|}}\ \ 1\ \overline{\underline{\left| 3\right|}} \\\\\\\\
\ 3\ \overline{\underline{\left| 1\right|}}\ \ 1\ \overline{\underline{\left| 2\right|}}\ \ 1\ \overline{\underline{\left| 3\right|}}\ \ 1\ \overline{\underline{\left| 4\right|}} \\\\\\\
4\ \overline{\underline{\left| 1\right|}}\ \ 1\ \overline{\underline{\left| 2\right|}}\ \ 2\ \overline{\underline{\left| 3\right|}}\ \ 1\ \overline{\underline{\left| 4\right|}} \\\\\\\
3\ \overline{\underline{\left| 1\right|}}\ \ 2\ \overline{\underline{\left| 2\right|}}\ \ 1\ \overline{\underline{\left| 3\right|}}\ \ 2\ \overline{\underline{\left| 4\right|}} \\\\\\\
2\ \overline{\underline{\left| 1\right|}}\ \ 3\ \overline{\underline{\left| 2\right|}}\ \ 2\ \overline{\underline{\left| 3\right|}}\ \ 1\ \overline{\underline{\left| 4\right|}} \\\\\\\\\\
\mbox{OPRIRE}\end{array} \)