The “comma sequence” starts with 1 and is defined by the property that if k and k′ are consecutive terms, the two-digit number formed from the last digit of k and the first digit of k′ is equal to the difference k′−k. If there is more than one such k′, choose the smallest, but if there is no such k′ the sequence terminates. The sequence begins 1, 12, 35, 94, 135, . . ., and, surprisingly, ends at term 2137453, which is 99999945. The paper analyzes the sequence and its generalizations to other starting values and other bases. A slight change in the rules allows infinitely long comma sequences to exist.
The comma sequence: a simple sequence with bizarre properties
Resta G.;
2024
Abstract
The “comma sequence” starts with 1 and is defined by the property that if k and k′ are consecutive terms, the two-digit number formed from the last digit of k and the first digit of k′ is equal to the difference k′−k. If there is more than one such k′, choose the smallest, but if there is no such k′ the sequence terminates. The sequence begins 1, 12, 35, 94, 135, . . ., and, surprisingly, ends at term 2137453, which is 99999945. The paper analyzes the sequence and its generalizations to other starting values and other bases. A slight change in the rules allows infinitely long comma sequences to exist.File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
2401.14346v2.pdf
accesso aperto
Tipologia:
Documento in Pre-print
Licenza:
Creative commons
Dimensione
276.81 kB
Formato
Adobe PDF
|
276.81 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
