A158288 - OEIS

%I #32 Jul 25 2024 02:43:09

%S 8,7,4,2,3,2,3,0,5,0,5,1,3,2,4,0,4,2,2,3,3,3,2,3,0,2,2,3,1,1,0,2,2,4,

%T 2,4,1,1,2,2,4,2,5,1,2,2,2,2,0,2,2,0,2,0,3,2,3,1,3,0,1,2,1,1,1,2,2,4,

%U 2,2,0,1,1,3,2,3,0,1,1,1,2,0,3,1,1,2,1,0,3,1,2,0,2,1,4,0,2,2,1,1,4,1,1,2,2

%N The number of twin prime pairs in the n-th century.

%C The number of members of A001359 from 100*n-99 to 100*n-3. - _Robert Israel_, Jul 19 2017

%H Robert Israel, <a href="/A158288/b158288.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A071538(100*n-3) - A071538(100*n-100). - _Robert Israel_, Jul 19 2017

%p f:= proc(n) local P;

%p    P:= select(isprime, {seq(i,i=100*n-99..100*n-1,2)});

%p    nops(P intersect map(`+`,P,2))

%p end proc:

%p map(f, [$1..200]); # _Robert Israel_, Jul 19 2017

%t Table[Count[Prime@ Range[Boole[n == 1] + PrimePi[100 (n - 1) + 1], PrimePi[100 n] - 1], _?(PrimeQ[# + 2] &)], {n, 105}] (* _Michael De Vlieger_, Jul 20 2017 *)

%o (PARI) a(n)=my(s=0);forprime(p=100*n-99,100*n-2,if(isprime(p+2),s++));s \\ _Charles R Greathouse IV_, Feb 03 2011

%o (Python)

%o from sympy import primerange, isprime

%o def a(n):

%o     s=0

%o     for p in primerange(100*n - 99, 100*n - 1):

%o         if isprime(p + 2):s+=1

%o     return s

%o print([a(n) for n in range(1, 201)]) # _Indranil Ghosh_, Jul 20 2017, after PARI code

%Y Cf. A001359, A071538.

%K nonn

%O 1,1

%A _Ki Punches_, Mar 15 2009

%E Corrected by _Ray Chandler_, May 23 2009