Cinquante signes

  Today we will play with a multi-digits combination lock. Our aim will be to produce prime integers – and only prime integers. We start, let's say, with a lock whose 10 disks display zero (disk can only display the 10 digits – no letters or symbols). 0000000000 We always read an integer from left to right, without considering the leading zeros. This is how the prime number 30307 is displayed, for instance: 0000030307 Starting with ten zeros, we are forced to use the rightmost disk to produce our first prime (using another disk would display a composite number – ending in zero). Say we start with 2: 000000000 2 (Note that once we have displayed a prime number p , we cannot reproduce it again.) As we want to produce a distinct prime, we have no choice here: we must rotate the rightmost disk again and stop elsewhere. Say we display 7: 000000000 7 Our collection of primes is rich now in two elements: 2 and 7. To produce another element, we have the choice – for the first time. We ca...

Formidable émission ce matin sur le marquis  Astolphe de Custine  dans l ’ émission de Jean-Noël  Jeanneney  sur France Q ( réécoute ic i ). L ’ extrait de la « lettre 25 » de Custine ouvrit la présentation du livre que Samanta Caretti , consacre au marquis. Enjoy – cet aristocrate écrit merveilleusement bien (et il a tout compris sur la Russie avant tout le monde !-) (...) Le Kremlin sur sa colline m’est apparu de loin comme une ville princière, bâtie au milieu de la ville populaire. Ce tyrannique château, cet orgueilleux monceau de pierres domine le séjour du commun des hommes de toute la hauteur de ses rochers, de ses murs et de ses campaniles, et contrairement à ce qui arrive aux monuments d’une dimension ordinaire, plus on approche de cette masse indestructible, et plus on est émerveillé. Tel que certains ossements d’animaux gigantesques, le Kremlin nous prouve l’histoire d’un monde dont nous ne pouvons nous empêcher de douter encore, même en en retrouvant les d...

Three sequences with sliding divider-digits A.  Lexicographically earliest sequence of distinct positive terms such that any digit “d” sliding “d” terms to the right divides the last term of the slip – except for the digit 0 that does not move and does nothing. B.  Lexicographically earliest sequence of distinct nonnegative terms such that any digit “d” sliding “d” terms to the left divides the last term of the slip – except for the digit 0 that does not move and does nothing C.  Lexicographically earliest sequence of distinct nonnegative terms such that any digit “d” sliding “d” terms either to the right or to the left divides the last term of the slip – except for the digit 0 that does not move and does nothing. A = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 24, 16, 36, 17, 20, 18, 22, 30, 42, 19, 84, 21, 28, 32, 40, … Check The 1 st digit of A is 1, slides 1 term to the right and divides the term 2: A = 1 , 2 , 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 24,...