cp's OEIS Frontend

A337769 Smallest integer m such that the sum of the first m prime numbers is greater than n^2.

%I A337769 #27 Apr 19 2022 00:01:38
%S A337769 1,2,3,4,5,6,7,8,9,10,10,11,12,12,13,14,15,15,16,17,18,18,19,20,20,21,
%T A337769 22,22,23,24,24,25,26,26,27,28,28,29,30,31,31,32,32,33,34,34,35,36,36,
%U A337769 37,38,38,39,40,40,41,41,42,43,43,44,45,45,46,46,47,48,48
%N A337769 Smallest integer m such that the sum of the first m prime numbers is greater than n^2.
%F A337769 a(n) = Min{m}, Sum_{i=1..m} prime(i) > n^2.
%F A337769 a(n) ~ sqrt(2)*n/sqrt(log n). - _Charles R Greathouse IV_, Apr 19 2022
%o A337769 (Python)
%o A337769 from sympy import prime
%o A337769 def sum_p(m):
%o A337769     sum1 = 0
%o A337769     for i in range(1, m+1):
%o A337769         sum1 += prime(i)
%o A337769     return sum1
%o A337769 pi = 1
%o A337769 for n in range(1, 101):
%o A337769     while sum_p(pi) <= n*n:
%o A337769         pi += 1
%o A337769     print(pi)
%o A337769 (PARI) a(n) = my(p=2, s=2); while(s <= n^2, p = nextprime(p+1); s += p); primepi(p); \\ _Michel Marcus_, Oct 26 2020
%o A337769 (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; if(n++>N, return(v)); n2=n^2)) \\ _Charles R Greathouse IV_, Apr 19 2022
%o A337769 (PARI) a(n)=my(n2=n^2, s, k); forprime(p=2, , s+=p; k++; if(s>n2, return(k))) \\ _Charles R Greathouse IV_, Apr 19 2022
%Y A337769 Cf. A000290, A007504.
%K A337769 nonn
%O A337769 1,2
%A A337769 _Ya-Ping Lu_, Oct 25 2020