cp's OEIS Frontend

A199323 Number of primes of the form n*(n+1)+2*k-3 with k from 1 to n+1.

%I A199323 #18 Jul 04 2013 13:40:16
%S A199323 1,2,3,2,3,4,3,4,5,3,5,5,5,5,6,5,6,6,6,8,8,5,7,10,7,8,7,10,7,9,11,10,
%T A199323 8,9,13,5,11,12,14,8,12,11,8,13,14,10,13,15,9,11,19,13,12,12,12,13,16,
%U A199323 14,16,16,13,18,15,16,12,17,16
%N A199323 Number of primes of the form n*(n+1)+2*k-3 with k from 1 to n+1.
%C A199323 n/log(n) is a good approximation of a(n) as n increases.
%H A199323 Pierre CAMI, <a href="/A199323/b199323.txt">Table of n, a(n) for n = 1..10000</a>
%F A199323 a(n) = pi(n^2 + 3n - 1) - pi(n^2 + n - 2) for n > 1. [_Charles R Greathouse IV_, Nov 11 2011]
%e A199323 Write the odd numbers like this :
%e A199323 1 3
%e A199323 5 7 9
%e A199323 11 13 15 17
%e A199323 19 21 23 25 27
%e A199323 29 31 33 35 37 39
%e A199323 41 43 45 47 49 51 53
%e A199323 .......................
%e A199323 line n : n*(n+1)+2*k-3 , k from 1 to n+1
%e A199323 line 1 , n=1 1*(1+1)*2*k-3  k=1 & k=2 , 3 prime a(1)=1
%e A199323 line 2 , n=2 for k=1 to 3 , 5 & 7 prime so a(2)=2
%e A199323 n=3 11 13 & 17 prime a(3)=3
%e A199323 n=4 19 & 23 prime a(4)=2
%e A199323 a(5)=3 , a(6)=4
%t A199323 npf[n_]:=Count[Table[n(n+1)+2k-3,{k,n+1}],_?PrimeQ]; Array[npf,70] (* _Harvey P. Dale_, Jul 04 2013 *)
%o A199323 (PARI) a(n)=if(n<4,n,primepi(n^2+3*n-1)-primepi(n^2+n-2)) \\ _Charles R Greathouse IV_, Nov 11 2011
%o A199323 (PARI) a(n)=my(s);forstep(a=n^2+n-1,n^2+3*n-1,2,s+=isprime(a)); s \\ _Charles R Greathouse IV_, Nov 11 2011
%K A199323 nonn
%O A199323 1,2
%A A199323 _Pierre CAMI_, Nov 06 2011