A057776 a(n) is the least number k such that prime(k) - 1 is divisible by 2^(n-1) and the quotient is odd.
1, 2, 3, 13, 7, 25, 44, 116, 55, 974, 1581, 2111, 1470, 4289, 10847, 15000, 6543, 91466, 62947, 397907, 498178, 1452314, 6025010, 20197904, 38946356, 9385401, 24843812, 98842359, 166808880, 556542914, 154570517, 3132108468, 7417604438, 3217817383, 47999122016
Offset: 1
Keywords
Examples
For n = 1, a(1) = 1, prime(a(1)) = prime(1) = 2 and prime(1)-1 = 1 is divisible by 2^(n-1) = 2^0 = 1; moreover 2 is the smallest. For n = 10, a(10) = 974, the 974th prime is 7681, prime(974) - 1 = 7680 = 512*15, is divisible by 2^9 = 512 and the quotient is 15, and there are no other primes such this below 7681. A057775(30) = 12348030977; a(30) = 556542914. It means that 12348030977 is the 556542914th prime. A057777(30) = 12348030976; when A057777(30) is divided by 2^29, the quotient is 23 = A057778(30).
Links
- Amiram Eldar, Table of n, a(n) for n = 1..72
Formula
a(n) = PrimePi(A057775(n-1)). - Amiram Eldar, Mar 16 2025
Extensions
a(32)-a(35) from Amiram Eldar, Mar 16 2025