|
%I #8 Jan 08 2020 16:27:12
%S 1,2,2,3,3,4,4,4,4,5,5,5,5,6,6,7,7,7,7,8,8,8,8,9,9,10,10,10,10,10,10,
%T 10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,
%U 13,14,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,15,16,16,16,16
%N Number of k (1 <= k <= n) such that k^2+1 is prime.
%F Hardy and Littlewood conjectured that : a(n) ~ c* sqrt(n)/Log(n) where c = prod(p prime, 1 - (-1)^((p-1)/2)/(p-1) ) = 1, 3727...
%t Accumulate[Table[If[PrimeQ[k^2+1],1,0],{k,80}]] (* _Harvey P. Dale_, Jan 08 2020 *)
%o (PARI) for(n=1,200,print1(sum(i=1,n,if(isprime(i^2+1)-1,0,1)),","))
%Y Cf. A005574, A002496.
%K easy,nonn
%O 1,2
%A _Benoit Cloitre_, Jun 09 2002
|
