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

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..72

Formula

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

Example

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).

Crossrefs

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

Sequence in context: A087564 A306431 A192362 * A110362 A393386 A074478

Adjacent sequences: A057773 A057774 A057775 * A057777 A057778 A057779

Keyword

nonn

Author

Labos Elemer, Nov 02 2000

Extensions

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

Status

approved