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A180259
Squares which are the sum of consecutive squares starting with 25^2.
3
625, 33124, 38025, 127449, 64529089, 81180100, 15884821225, 3370675683600
OFFSET
1,1
COMMENTS
That is, terms are squares of the form sum_{i=25..m} i^2 = (m-24) *(2*m^2+51*m+1225) / 6 for some m. Known solutions refer to m = 25, 48, 50, 73, 578, 624, 3625 and 21624, and no further in the range m <= 70000000.
This sequence is complete. See A180442 and A184763.
EXAMPLE
38025 is in the sequence because 38025 = 195^2 = 25^2 + 26^2 + ... + 50^2.
MATHEMATICA
Select[Accumulate[Range[25, 22000]^2], IntegerQ[Sqrt[#]] &] (* Harvey P. Dale, Aug 10 2023 *)
PROG
(PARI) for(n=26, 9999999, t=n*(n+1)*(2*n+1)/6-4900; if(issquare(t), print1(t, ", ")))
CROSSREFS
KEYWORD
nonn,fini,full
AUTHOR
Zhining Yang, Jan 17 2011
STATUS
approved