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

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

Offset

1,1

Comments

The set of squares in A071148, i.e., intersection of A000290 and A071148. [extended by 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

Links

Table of n, a(n) for n=1..8.

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

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A147883 A166964 A316337 * A063797 A231761 A098207

Adjacent sequences: A274117 A274118 A274119 * A274121 A274122 A274123

Keyword

nonn,more

Author

K. D. Bajpai, Jun 10 2016

Extensions

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

Status

approved