cp's OEIS Frontend

A353024 Largest k such that A007504(k) <= n^2.

%I A353024 #25 Apr 19 2022 07:39:40
%S A353024 0,1,2,3,4,5,6,7,8,9,9,10,11,11,12,13,14,14,15,16,17,17,18,19,19,20,
%T A353024 21,21,22,23,23,24,25,25,26,27,27,28,29,30,30,31,31,32,33,33,34,35,35,
%U A353024 36,37,37,38,39,39,40,40,41,42,42,43,44,44,45,45,46,47,47
%N A353024 Largest k such that A007504(k) <= n^2.
%F A353024 a(n) = A337769(n) - 1.
%F A353024 a(n) ~ sqrt(2)*n/sqrt(log n). - _Charles R Greathouse IV_, Apr 18 2022
%F A353024 a(n) = A350174(n^2). - _Kevin Ryde_, Apr 19 2022
%o A353024 (Python)
%o A353024 from sympy import prime
%o A353024 def a(n):
%o A353024     k = 1
%o A353024     total = 0
%o A353024     while True:
%o A353024         total += prime(k)
%o A353024         if total > n**2:
%o A353024             break
%o A353024         k += 1
%o A353024     return k-1
%o A353024 (PARI) first(N)=my(v=vector(N),s,k,n=1,n2=1); forprime(p=2,, s+=p; k++; while(s>n2, v[n]=k-1; if(n++>N, return(v)); n2=n^2)) \\ _Charles R Greathouse IV_, Apr 18 2022
%o A353024 (PARI) a(n)=my(n2=n^2,s,k); forprime(p=2,, s+=p; k++; if(s>n2, return(k-1))) \\ _Charles R Greathouse IV_, Apr 18 2022
%Y A353024 Cf. A000290, A007504, A337769, A350174, A033997.
%K A353024 nonn
%O A353024 1,3
%A A353024 _Joelle H. Kassir_, Apr 17 2022