A205001 Least k such that n divides the k-th difference between distinct triangular numbers.

1, 1, 3, 6, 2, 8, 5, 28, 4, 11, 14, 8, 20, 7, 13, 120, 35, 12, 44, 11, 26, 18, 65, 34, 17, 25, 16, 49, 104, 24, 119, 496, 23, 42, 22, 58, 170, 52, 31, 41, 209, 30, 230, 29, 40, 75, 275, 134, 39, 62, 50, 38, 350, 37, 74, 49, 61, 117, 434, 48

Offset: 1

Author

Clark Kimberling, Jan 21 2012

Keywords

• nonn

Comments

For a guide to related sequences, see A204892.

Examples

			The triangular numbers: s(k)=k(k+1)/2.
Their differences, ordered as in A193974:
u(1)=s(2)-s(1)=2
u(2)=s(3)-s(1)=5
u(3)=s(3)-s(2)=3
u(4)=s(4)-s(1)=9
u(5)=s(4)-s(2)=7
u(6)=s(4)-s(3)=4.
a(1)=1 because 1 divides u(1)
a(2)=1 because 2 divides u(1)
a(3)=3 because 3 divides u(3)
a(4)=6 because 4 divides u(6)
a(5)=2 because 5 divides u(2)
a(6)=8 because 6 divides u(8)
		

Crossrefs

Cf. A205002, A204892.

Programs

Mathematica

(See the program at A205002.)