A309655 -id:A309655 - cp's OEIS frontend

A309714 The smallest possible nonnegative difference between the sum of the first n positive integers (A000217) and the sum of any number of the directly following and consecutive integers.

1, 0, 2, 5, 2, 6, 1, 6, 12, 5, 12, 3, 11, 0, 9, 19, 6, 17, 2, 14, 27, 10, 24, 5, 20, 36, 15, 32, 9, 27, 2, 21, 41, 14, 35, 6, 28, 51, 20, 44, 11, 36, 1, 27, 54, 17, 45, 6, 35, 65, 24, 55, 12, 44, 77, 32, 66, 19, 54, 5, 41, 78, 27, 65, 12, 51, 91, 36, 77, 20, 62

Offset: 1

Bob Andriesse, Aug 13 2019

nonn

a(n) = 0 if a positive integer m exists, such that m * (m + 1) = 2 * n * (n + 1). Let k = m - n, then n = (2 * k - 1 + sqrt(8 * k^2 + 1)) / 2. All k for which 8 * k^2 + 1 is a perfect square (A001109) yield a value for n for which a(n) = 0.

a(A053141(n)) = 0 for all n.

			a(2) = 1 + 2 - 3 = 0;
a(3) = 1 + 2 + 3 - 4 = 2;
a(7) = 1 + 2 + 3 + 4 + 5 + 6 + 7 - (8 + 9 + 10) = 1.
a(A053141(2)) = a(14) = 0, because A000217(20) = 2 * A000217(14).

Cf. A000217, A001109, A001652, A053141, A309655.

a(n) = {my(t=n*(n+1)/2, k = n+1); while(t >= k, t -= k; k++); t;} \\ Michel Marcus, Aug 16 2019

cp's OEIS Frontend

A309714 The smallest possible nonnegative difference between the sum of the first n positive integers (A000217) and the sum of any number of the directly following and consecutive integers.

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