A363709 For n >= 0, a(n) is the least integer i >= 0 such that n + (n + 1) + ... + (n + i) is a prime number or a(n) = -1 if no such i exists.

2, 1, 0, 0, -1, 0, 1, 0, 1, 1, -1, 0, -1, 0, 1, 1, -1, 0, 1, 0, 1, 1, -1, 0, -1, -1, 1, -1, -1, 0, 1, 0, -1, 1, -1, 1, 1, 0, -1, 1, -1, 0, -1, 0, 1, -1, -1, 0, 1, -1, 1, 1, -1, 0, 1, -1, 1, -1, -1, 0, -1, 0, -1, 1, -1, 1, -1, 0, 1, 1, -1, 0, -1, 0, 1, 1, -1, -1, 1, 0, -1

Offset: 0

Author

Ctibor O. Zizka, Jun 17 2023

Keywords

• sign

Comments

Shortest arithmetic sequence with initial term n and difference 1 that sums to a prime number.

For n = 0, a(n) = 2.

For n >= 1, a(n) < 2.

For n in A053176 or A005384, a(n) = 0.

For n in A067812, a(n) = 1.

For n in A077654, a(n) = -1.

Examples

			n = 4: no such i exists, thus a(4) = -1.
n = 5: n is prime, i = 0, thus a(5) = 0.
n = 6: n + (n + 1) = 6 + 7 = 13 is prime, i = 1, thus a(6) = 1.
		

Crossrefs

Cf. A000040, A005384, A053176, A067812, A077654.

Formula

((i + 1)*(i + 2*n))/2 = p, p prime number.