Steinhaus sequence - Colegiul Ortodox "Mitropolitul Nicolae Colan" (Cluj-Roumanie) Lycée Marseilleveyre (Marseille), Lycée Victor Hugo (Marseille)

Colegiul Ortodox "Mitropolitul Nicolae Colan" (Cluj-Roumanie)
Hugo Steinhaus (1887-1972), One Hundred Problems in Elementary Mathematics, 1963.
We write the two numbers 2 and 3: 23.
We take these two numbers, calculate their product 2 × 3 = 6 and write it down: 236.
We take the numbers 3 (again) and 6, calculate their product 3 × 6 = 18 and write it on the back: 23618.
We take the numbers 6 and 1, calculate their product 6 × 1 = 6 and write it as: 236186.
We repeat the process endlessly, this produces a series of numbers:
Is this sequence really infinite? What numbers appear in it? We notice blocks of consecutive identical numbers: 22, 6666666. Other numbers form do they have blocks like this? How many repetitions can there be? And if we change the starting numbers, what can happen?

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Bénédicte Espariat

jeu 14/03/2024 - 00:47

Le lycée Victor Hugo n'est pas jumelé avec ce sujet

Pour Marseilleveyre il y a 7 élèves à rajouter au 2 élèves roumains donc 9 en tout