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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.
0
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
0,1
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.
FORMULA
((i + 1)*(i + 2*n))/2 = p, p prime number.
EXAMPLE
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
KEYWORD
sign
AUTHOR
Ctibor O. Zizka, Jun 17 2023
STATUS
approved