Meaning of Carol number | Babel Free

Definitions

An integer of the form 4ⁿ-2ⁿ⁺¹-1.

Examples

“Mathematically, it is actually interesting in all sorts of ways, being both a Keith number⟳ and a Carol number⟳.”

“[…] 7. There are 47 occurrences of 47 in the first thousand prime numbers. 8. The atomic number⟳ of Silver is 47. 9. It is a Carol number⟳. […]”

“In 2007 the largest Carol number⟳ was found for n = 253987, consisting of 152916 digits, by using the programs MultiSieve and PrimeFormGW.”

“For ngt;2, the binary representation of the n-th Carol number⟳ is n-2 consecutive unities, a single zero in the middle, and n#43;1 more consecutive unities, or to put⟳ it algebraically, #92;textstyle#123;CN(n)#61;#92;sum#95;#123;i#61;1,i#92;nen#43;2#125;#123;2n#125;2#123;i-1”

CEFR level