Репдиджит

В развлекателната математика, репдиджит или понякога монодиджит – е естествено число, състоящо се само от една и съща цифра в позиционна бройна система (например десетична).[1] Думата е съставена от английските думи repeat, „повторение“ и digit, „цифра“.[2]

Примери са 11, 666, 4444 и 999999. Всички репдиджити са палиндромни числа и са кратни на репюнита със същата дължина. Два от най-известните репдиджити са 666, посочено в християнската Есхатологията като числото на звяра, и 777, което понякога е считано за „щастливо число“, заради употребата му в повечето игрални автомати за отбелязване на джакпота. Други известни репдиджити са простите репюнит числа и особено мерсеновите прости числа (които са репдиджити в двоичната система).

Репдиджит в бройната система е , където е повтарящата се цифра, а е броят на повторенията. Например, репдиджитът 77777 в десетичната система е .

Триъгълни репдиджит числа

Триъгълно число[3] е всяко число от поредицата, съответстваща на броя на точките образуващи равностранен триъгълник.

Според последователност A045914 в OEIS има само 7 числа, които са едновременно триъгълни и репдиджит:

0, 1, 3, 6, 55, 66, 666

В случая е включена 0 като сума на цифрите в триъгълник със страна 0. Също така са включени и едноцифрените числа, тъй като технически те са репдиджит само от една цифра и също са триъгълни.

Вижте също

Източници

  1. ↑ Наталья Карпушина. Вне формата. Занимательная математика: гимнастика для ума или искусство удивлять?
  2. ↑ Beiler, Albert. Recreations in the Theory of Numbers: The Queen of Mathematics Entertains. 2. New York, Dover Publications, 1966. ISBN 978-0-486-21096-4. с. 83.
  3. ↑ Как да преброим числата, без да ги броим или защо математиката е красива

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