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%I #16 Mar 30 2015 21:41:36
%S 1,2,2,6,4,8,5,12,22,8,27,21,11,23,38,36,16,43,31,15,52,36,52,75,45,
%T 22,42,19,48,160,47,81,22,141,26,90,89,65,102,96,40,180,40,73,38,227,
%U 227,85,44,85,129,43,216,133,140,137,45,147,105,46,260,354,115,52,108,386,165,283,64
%N Number of primes between prime(n)^2 and prime(n)*prime(n+1).
%H Antti Karttunen, <a href="/A256468/b256468.txt">Table of n, a(n) for n = 1..6542</a>
%H A. Karttunen, <a href="https://oeis.org/plot2a?name1=A256468&name2=A256469&tform1=untransformed&tform2=untransformed&shift=0&radiop1=ratio&drawlines=true">Ratio a(n)/A256469(n) plotted with OEIS Plot2-script</a>
%H A. Karttunen, <a href="https://oeis.org/plot2a?name1=A256468&name2=A050216&tform1=untransformed&tform2=untransformed&shift=0&radiop1=ratio&drawlines=true">Ratio a(n)/A050216(n) plotted with OEIS Plot2-script</a>
%F a(n) = A256447(n)-1.
%F a(n) = A050216(n) - A256469(n).
%F a(n) = A256469(n) - A256470(n).
%t Table[Abs@ Subtract[PrimePi[Prime[n]^2], PrimePi[Prime[n] Prime[n + 1]]], {n, 69}] (* _Michael De Vlieger_, Mar 30 2015 *)
%o (PARI)
%o allocatemem(234567890);
%o default(primelimit,4294965247);
%o A256468(n) = (primepi(prime(n)*prime(n+1)) - primepi(prime(n)^2));
%o for(n=1, 6542, write("b256468.txt", n, " ", A256468(n)));
%o (Scheme) (define (A256468 n) (let* ((p (A000040 n)) (p2 (* p p))) (let loop ((s 0) (k (* p (A000040 (+ 1 n))))) (cond ((= k p2) s) (else (loop (+ s (if (prime? k) 1 0)) (- k 1)))))))
%Y One less than A256447.
%Y Cf. A050216, A256469, A256470.
%K nonn
%O 1,2
%A _Antti Karttunen_, Mar 30 2015
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