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A274120
Squares that are the sum of the first n odd primes for some n.
1
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
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
KEYWORD
nonn,more
AUTHOR
K. D. Bajpai, Jun 10 2016
EXTENSIONS
Second comment rephrased by Harvey P. Dale, May 26 2023
STATUS
approved