A236469 Primes p such that pi(p) = floor(p/10), where pi is the prime counting function.

64553, 64567, 64577, 64591, 64601, 64661

Offset

1,1

Comments

No further term below 32452843.

The first three terms in the sequence are consecutive primes.

Is this sequence finite?

No further term below 179424673.

The prime number theorem implies that this sequence is finite. Rosser proves that pi(x) < x/(log x - 4) for x >= 55, which can be used to show that there are no more terms. - Eric M. Schmidt, Aug 04 2014

Links

Table of n, a(n) for n=1..6.

J. B. Rosser. Explicit bounds for some functions of prime numbers. Amer. J. Math. 63 (1941), 211-232.

Maple

KD := proc() local a, b; a:=ithprime(n); b:=floor(a/10); if n=b then RETURN (a); fi; end: seq(KD(), n=1..1000000);

Mathematica

Do[p = Prime[n]; k = Floor[p/10]; If[k == n, Print[p]], {n, 10^6}] (* Bajpai *)
Select[Prime[Range[6500]], PrimePi[#] == Floor[#/10] &] (* Alonso del Arte, Jan 26 2014 *)

Crossrefs

Cf. A075902, A114924, A067248.

Sequence in context: A205631 A205333 A165689 * A203712 A061738 A350800

Adjacent sequences: A236466 A236467 A236468 * A236470 A236471 A236472

Keyword

nonn,less,fini,full

Author

K. D. Bajpai, Jan 26 2014

Status

approved