A049386 Binary order of 2^n-th prime.

1, 2, 3, 5, 6, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72

Offset: 0

Author

Labos Elemer

Keywords

• nonn

Examples

			The 549755813888th = (2^39)th prime is 16149760533341, whose binary order is 44: it is ceiling(43.87657801)=44, so a(39)=44;
a(0)=1 is the binary order of the (2^0)th = 1st prime (= 2), which is log_2(2) = 1.
		

Links

• Jinyuan Wang, Table of n, a(n) for n = 0..78

Crossrefs

Cf. A006988, A029837, A033844.

Programs

PARI

a(n) = ceil(log(prime(2^n))/log(2)); \\ Michel Marcus, Aug 07 2021

Formula

a(n) = A029837(A033844(n)).

a(n) = ceiling(log_2(prime(2^n))).

Extensions

a(40)-a(57) from Michel Marcus, Aug 25 2019

More terms from Jinyuan Wang, Aug 07 2021