A158288 The number of twin prime pairs in the n-th century.

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, 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, 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

Offset: 1

Author

Ki Punches, Mar 15 2009

Keywords

• nonn

Comments

The number of members of A001359 from 100*n-99 to 100*n-3. - Robert Israel, Jul 19 2017

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001359, A071538.

Programs

Maple

f:= proc(n) local P;
   P:= select(isprime, {seq(i,i=100*n-99..100*n-1,2)});
   nops(P intersect map(`+`,P,2))
end proc:
map(f, [$1..200]); # Robert Israel, Jul 19 2017

Mathematica

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 *)

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

Python

from sympy import primerange, isprime
def a(n):
    s=0
    for p in primerange(100*n - 99, 100*n - 1):
        if isprime(p + 2):s+=1
    return s
print([a(n) for n in range(1, 201)]) # Indranil Ghosh, Jul 20 2017, after PARI code

Formula

a(n) = A071538(100*n-3) - A071538(100*n-100). - Robert Israel, Jul 19 2017

Extensions

Corrected by Ray Chandler, May 23 2009