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Number of twin primes between n and n^2. Only smaller of twins (terms of A001359) are counted.
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%I #8 Sep 08 2022 08:45:37

%S 0,1,2,2,3,3,4,5,6,6,8,8,9,11,12,14,16,16,17,17,19,20,21,22,24,26,26,

%T 26,29,30,30,31,34,36,36,39,41,42,45,45,48,49,50,53,55,59,61,63,66,66,

%U 68,70,74,74,76,77,78,83,87,90,91,93,96,100

%N Number of twin primes between n and n^2. Only smaller of twins (terms of A001359) are counted.

%H Amiram Eldar, <a href="/A143738/b143738.txt">Table of n, a(n) for n = 1..10000</a>

%e For n = 6, between 6 and 36 the smaller of twin pairs are {11, 17, 29}, so a(6) = 3.

%t Table[Count[Table[PrimeQ[j] && PrimeQ[j + 2], {j, n, n*n}], True], {n, 1, 100}]

%o (Magma) [#[p:p in PrimesInInterval(n,n^2)|IsPrime(p+2)]:n in [1..80]]; // _Marius A. Burtea_, Dec 20 2019

%Y Cf. A001359, A080356.

%K nonn

%O 1,3

%A Alen Skugor (askugor(AT)gmail.com), Aug 30 2008