A273874 - OEIS

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.

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

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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.

LINKS

Table of n, a(n) for n=1..85.

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

Cf. A000404, A034705.

Sequence in context: A156952 A158748 A351241 * A086039 A265824 A097413

Adjacent sequences: A273871 A273872 A273873 * A273875 A273876 A273877

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