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

2, 5, 7, 11, 17, 23, 29, 37, 41, 53, 59, 71, 83, 97, 103, 127, 131, 149, 163, 179, 191, 211, 223, 239, 257, 277, 307, 317, 337, 353, 373, 397, 419, 443, 467, 491, 521, 541, 569, 593, 617, 643, 673, 701, 727, 757, 787, 821, 853, 877, 907, 937

Offset: 1

Author

Dimitris Valianatos, Jul 17 2017

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A076873.

Programs

Mathematica

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 *)
spn[n_]:=Module[{k=Ceiling[Sqrt[n]]},If[PrimeQ[k],k,NextPrime[k]]]; spn/@ Accumulate[Prime[Range[60]]^2] (* Harvey P. Dale, May 20 2021 *)

PARI

{
sp=0;p=0;
forprime(n=2,200,
         sp+=n^2;
         while(p^2
				

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

Extensions

Definition clarified by Felix Fröhlich, Jul 18 2017