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

Author

K. D. Bajpai, Jan 26 2014

Keywords

• nonn
• less
• fini
• full

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

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

Crossrefs

Cf. A075902, A114924, A067248.

Programs

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 *)