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A236469
Primes p such that pi(p) = floor(p/10), where pi is the prime counting function.
0
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
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
KEYWORD
nonn,less,fini,full
AUTHOR
K. D. Bajpai, Jan 26 2014
STATUS
approved