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%I #21 Aug 04 2014 05:23:03
%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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