A Kynea number is an integer of the form
An equivalent formula is
The sequence of Kynea numbers starts with:
The binary representation of the nth Kynea number is a single leading one, followed by n - 1 consecutive zeroes, followed by n + 1 consecutive ones, or to put it algebraically:
Prime Kynea numbersEdit
Starting with 7, every third Kynea number is a multiple of 7. Thus, for a Kynea number to be a prime number, its index n cannot be of the form 3x + 1 for x > 0. The first few Kynea numbers that are also prime are 7, 23, 79, 1087, 66047, 263167, 16785407 (sequence A091514 in the OEIS).
As of July 2019[update], the largest known prime Kynea number has index n = 852770, which has 513419 digits. It was found by Ryan Propper in July 2019 using the programs CKSieve and PrimeFormGW. It is the 51st Kynea prime.