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%I #27 Apr 19 2022 00:01:38
%S 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 22,22,23,24,24,25,26,26,27,28,28,29,30,31,31,32,32,33,34,34,35,36,36,
%U 37,38,38,39,40,40,41,41,42,43,43,44,45,45,46,46,47,48,48
%N Smallest integer m such that the sum of the first m prime numbers is greater than n^2.
%F a(n) = Min{m}, Sum_{i=1..m} prime(i) > n^2.
%F a(n) ~ sqrt(2)*n/sqrt(log n). - _Charles R Greathouse IV_, Apr 19 2022
%o (Python)
%o from sympy import prime
%o def sum_p(m):
%o sum1 = 0
%o for i in range(1, m+1):
%o sum1 += prime(i)
%o return sum1
%o pi = 1
%o for n in range(1, 101):
%o while sum_p(pi) <= n*n:
%o pi += 1
%o print(pi)
%o (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 (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 (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 Cf. A000290, A007504.
%K nonn
%O 1,2
%A _Ya-Ping Lu_, Oct 25 2020
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