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

Author

Labos Elemer, Nov 02 2000

Keywords

• nonn

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

Crossrefs

Cf. A000040, A000720, A006093, A057773, A057775, A057776, A057777, A057778.

Formula

a(n) = PrimePi(A057775(n-1)). - Amiram Eldar, Mar 16 2025

Extensions

a(32)-a(35) from Amiram Eldar, Mar 16 2025