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A273874
Least positive integer k such that k^2 + (k+1)^2 + ... + (k+n-2)^2 + (k+n-1)^2 is the sum of two nonzero squares. a(n) = 0 if no solution exists.
0
5, 1, 2, 0, 2, 0, 0, 0, 0, 2, 5, 1, 12, 0, 3, 0, 3, 0, 0, 0, 0, 0, 53, 1, 1, 1, 2, 0, 4, 0, 0, 0, 5, 2, 0, 0, 2, 0, 3, 0, 5, 0, 0, 5, 0, 0, 73, 1, 3, 1, 2, 0, 2, 0, 5, 0, 0, 2, 97, 1, 4, 0, 0, 0, 2, 5, 0, 0, 30, 0, 0, 0, 1, 1, 4, 0, 0, 0, 0, 0, 0, 2, 26, 0, 6
OFFSET
1,1
COMMENTS
Least positive integer k such that Sum_{i=0..n-1} (k+i)^2 = n*(6*k^2 + 6*k*n - 6*k + 2*n^2 - 3*n + 1)/6 is the sum of two nonzero squares. a(n) = 0 if no k exists for corresponding n.
EXAMPLE
a(1) = 5 because 5^2 = 3^2 + 4^2.
a(3) = 2 because 2^2 + 3^2 + 4^2 = 2^2 + 5^2.
CROSSREFS
Sequence in context: A156952 A158748 A351241 * A086039 A265824 A097413
KEYWORD
nonn
AUTHOR
Altug Alkan, Jun 02 2016
EXTENSIONS
a(7)-a(50) from Giovanni Resta, Jun 02 2016
More terms from Jinyuan Wang, May 02 2021
STATUS
approved