A274120 - OEIS

%I #24 May 26 2023 17:35:49

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

%N Squares that are the sum of the first n odd primes for some n.

%C The set of squares in A071148, i.e., intersection of A000290 and A071148. [extended by _Felix Fröhlich_, Jun 10 2016]

%C 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

%H G. L. Honaker Jr. and C. Caldwell, <a href="https://t5k.org/curios/page.php?number_id=4306">Prime Curios! : 961</a>

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

%t Select[s=0;Table[s=s+Prime[k],{k,2,15000000}],IntegerQ[Sqrt[#]]&]

%t Select[Accumulate[Prime[Range[2,100000]]],IntegerQ[Sqrt[# ]]&] (* _Harvey P. Dale_, May 26 2023 *)

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

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

%K nonn,more

%O 1,1

%A _K. D. Bajpai_, Jun 10 2016

%E Second comment rephrased by _Harvey P. Dale_, May 26 2023