

A131872


Set m = 0, n = 1. Find smallest k >= 2 such that pi(k) = (kpi(k))  (mpi(m)); set a(n) = pi(k), m = k, n = n+1. Repeat.


0



1, 4, 8, 11, 16, 23, 30, 39, 50, 62, 78, 97, 119, 141, 172, 205, 242, 284, 334, 393, 455, 531, 615, 704, 811, 928, 1059, 1213, 1373, 1560, 1761, 1988, 2239, 2524, 2833, 3180, 3557, 3983, 4448, 4942, 5503, 6126, 6791, 7522, 8331, 9228, 10188, 11228
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OFFSET

1,2


COMMENTS

For n>1, a(n)a(n1) is approximately pi(n)^2/n.


LINKS

Table of n, a(n) for n=1..48.
A. Granville and G. Martin, Prime number races
Eric Weisstein's World of Mathematics, Prime Counting Function


EXAMPLE

m=0, n=1; pi(2) = (21)(0) = 1 = number of nonprimes from 1 to 2, a(1) = 1 is a term. Now n=2, m=2.
pi(9) = (94)(21) = 4 = number of nonprimes from 3 to 9, a(2) = 4 is a term. Now n=3, m=9.
pi(21) = (218)(94) = 8 = number of nonprimes from 10 to 21, a(3) = 8 is a term.


MATHEMATICA

m=0; Do[If[PrimePi[n]==(nPrimePi[n])(mPrimePi[m]), Print[PrimePi[n]]; m=n], {n, 1, 10^6, 1}]


CROSSREFS

Cf. A000720, A062298.
Sequence in context: A267534 A186147 A023491 * A104655 A046898 A171070
Adjacent sequences: A131869 A131870 A131871 * A131873 A131874 A131875


KEYWORD

nonn


AUTHOR

Manuel Valdivia, Oct 05 2007


EXTENSIONS

Edited by N. J. A. Sloane, Nov 05 2007


STATUS

approved



