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A236469 Primes p such that pi(p) = floor(p/10), where pi is the prime counting function. 0

%I

%S 64553,64567,64577,64591,64601,64661

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

%C No further term below 32452843.

%C The first three terms in the sequence are consecutive primes.

%C Is this sequence finite?

%C No further term below 179424673.

%C 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

%H J. B. Rosser. <a href="http://dx.doi.org/10.2307/2371291">Explicit bounds for some functions of prime numbers</a>. Amer. J. Math. 63 (1941), 211-232.

%p 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);

%t Do[p = Prime[n]; k = Floor[p/10]; If[k == n, Print[p]], {n, 10^6}] (* Bajpai *)

%t Select[Prime[Range[6500]], PrimePi[#] == Floor[#/10] &] (* _Alonso del Arte_, Jan 26 2014 *)

%Y Cf. A075902, A114924, A067248.

%K nonn,less,fini,full

%O 1,1

%A _K. D. Bajpai_, Jan 26 2014

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Last modified November 12 09:29 EST 2019. Contains 329054 sequences. (Running on oeis4.)