A274120 Squares that are the sum of the first k odd primes for some k.

961, 1369, 1849, 4225, 263169, 130919364, 758451600, 29682949232484409

Offset: 1

Author

K. D. Bajpai, Jun 10 2016

Keywords

• nonn
• more

Comments

Intersection of A000290 and A071148. [Felix Fröhlich, Jun 10 2016]

a(9), if it exists, is larger than 2*10^26 and would require adding more than 3.6*10^12 primes. - Giovanni Resta, Jun 12 2016

Examples

			961 is in the sequence because 961 = 31^2. Also, 3+5+7+...+83+89 = 961.
		

Links

• G. L. Honaker Jr. and C. Caldwell, Prime Curios! : 961

Crossrefs

Cf. A007504, A033997, A061890, A065091, A071148.

Programs

Mathematica

Select[s=0;Table[s=s+Prime[k],{k,2,15000000}],IntegerQ[Sqrt[#]]&]
Select[Accumulate[Prime[Range[2,100000]]],IntegerQ[Sqrt[# ]]&] (* Harvey P. Dale, May 26 2023 *)

PARI

my(s = 0); forprime(p=3, 1e10, s += p; if (issquare(s), print1(s, ", ")))

Extensions

Second comment rephrased by Harvey P. Dale, May 26 2023