A122933 a(n)-th prime is equal to the sum_{i=1..k} pi(i) for some k (cf. A000720).

2, 3, 5, 8, 9, 12, 14, 18, 23, 28, 42, 58, 61, 70, 91, 95, 101, 103, 132, 142, 150, 161, 167, 170, 248, 347, 361, 382, 409, 412, 424, 463, 476, 514, 532, 561, 645, 666, 710, 724, 736, 788, 795, 869, 999, 1010, 1083, 1106, 1124, 1136, 1143, 1149, 1163, 1205, 1244

Offset: 1

Author

Alexander Adamchuk, Sep 20 2006

Keywords

• nonn

Comments

A046992 is sum_{k=1..n} pi(k). A122516 are the members of A046992 which are primes.

Primes in A046992[n] are {3,5,11,19,23,37,43,61,...} = A122516[n] = Prime[a(n)].

Examples

			A122516[n] begins {3,5,11,19,23,37,43,61,83,107,181,271,...}.
So a(1) = 2 because A122516[1] 3 = Prime[2].
a(2) = 3 because A122516[2] = 5 = Prime[3].
a(3) = 5 because A122516[3] = 11 = Prime[5].
		

Crossrefs

Cf. A122516, A046992, A000720, A020641.

Programs

Mathematica

PrimePi[Flatten[Table[If[PrimeQ[Sum[ PrimePi[n], {n, 1, m}]], Sum[PrimePi[n], {n, 1, m}], {}], {m, 1, 500}]]]

Formula

a(n) = PrimePi[ A122516[n] ].

Extensions

Edited by Robert G. Wilson v, Sep 28 2006