A103960 - OEIS

%I #9 Jul 30 2015 15:37:18

%S 1,1,2,2,2,3,1,2,4,3,2,5,3,3,5,3,4,4,4,5,6,3,4,6,3,5,6,5,3,6,5,8,5,5,

%T 6,5,7,9,7,6,6,5,7,6,8,5,8,10,5,6,8,6,7,7,10,10,3,11,8,11,6,10,8,12,9,

%U 9,7,11,9,7,8,9,6,14,8,10,11,11,12,11,7,8

%N Number of primes p such that prime(n)*p - 2 is prime and p <= prime(n).

%C Conjecture: All items of this sequence are greater than or equal to 1. Tested to prime(1000000).

%C a(A137291(n)) = A210481(A137291(n)) + 1. - _Reinhard Zumkeller_, Jul 30 2015

%H T. D. Noe, <a href="/A103960/b103960.txt">Table of n, a(n) for n = 1..1000</a>

%e Prime(1)*2-2 = 2, so a(1)=1;

%e Prime(3) = 5, 5*3-2 = 13, 5*5-2 = 23, so a(3)=2;

%t Table[p=Prime[n]; ct=0; Do[pk=Prime[k]; If[PrimeQ[p*pk-2], ct=ct+1], {k, n}]; ct, {n, 100}]

%o (Haskell)

%o a103960 n = sum [a010051' $ p * q - 2 |

%o                  let p = a000040 n, q <- takeWhile (<= p) a000040_list]

%o -- _Reinhard Zumkeller_, Jul 30 2015

%Y Cf. A103959.

%Y  Cf. A010051, A000040, A137291, A210481.

%K easy,nonn

%O 1,3

%A _Lei Zhou_, Feb 22 2005