Carol number

plural Carol numbers

1. mathematicsAn integer of the form 4ⁿ-2ⁿ⁺¹-1.

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

   2009, The Philosophers' Magazine - Issue 47, page 4

   3 more examples

   […] 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. […]

   2014, Rajesh Kumar Thakur, The Power of Mathematical Numbers, page 131

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

   2019, Dr. Ir. Maarten Looijen, Over getallen gesproken - Talking about numbers, page 70

   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

   2021, Elena Deza, Mersenne Numbers And Fermat Numbers, page 136