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A290012 a(n) is the smallest prime number p satisfying p^2 >= Sum_{1 <= k <= n} prime(k)^2. 0

%I

%S 2,5,7,11,17,23,29,37,41,53,59,71,83,97,103,127,131,149,163,179,191,

%T 211,223,239,257,277,307,317,337,353,373,397,419,443,467,491,521,541,

%U 569,593,617,643,673,701,727,757,787,821,853,877,907,937

%N a(n) is the smallest prime number p satisfying p^2 >= Sum_{1 <= k <= n} prime(k)^2.

%C Conjecture: The only twin prime pair in the sequence is (5, 7).

%e The prime number 17 is the fifth term because the sum of squares of the first 5 prime numbers is 2^2 + 3^2 + 5^2 + 7^2 + 11^2 = 208 < 17^2 = 289.

%t Table[Function[k, p = 2; While[p^2 < k, p = NextPrime@ p]; p][Total[Prime[Range@ n]^2]], {n, 52}] (* _Michael De Vlieger_, Jul 18 2017 *)

%o (PARI) {

%o sp=0;p=0;

%o forprime(n=2,200,

%o sp+=n^2;

%o while(p^2<sp,p=nextprime(p+1));

%o print1(p", ")

%o )

%o }

%o (PARI) a(n) = my(s=sum(k=1, n, prime(k)^2)); forprime(p=1, , if(p^2 >= s, return(p))) \\ _Felix Fröhlich_, Jul 18 2017

%Y Cf. A076873.

%K nonn

%O 1,1

%A _Dimitris Valianatos_, Jul 17 2017

%E Definition clarified by _Felix Fröhlich_, Jul 18 2017

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Last modified April 8 04:26 EDT 2020. Contains 333312 sequences. (Running on oeis4.)