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

1,3

Comments

For a guide to related sequences, see A204892.

Links

Table of n, a(n) for n=1..60.

Example

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)

Mathematica

(See the program at A205002.)

Crossrefs

Cf. A205002, A204892.

Sequence in context: A244619 A330576 A099506 * A154204 A309609 A266971

Adjacent sequences: A204998 A204999 A205000 * A205002 A205003 A205004

Keyword

nonn

Author

Clark Kimberling, Jan 21 2012

Status

approved