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Least k such that n divides the k-th difference between distinct triangular numbers.
1

%I #6 Feb 27 2013 09:44:10

%S 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,

%T 16,49,104,24,119,496,23,42,22,58,170,52,31,41,209,30,230,29,40,75,

%U 275,134,39,62,50,38,350,37,74,49,61,117,434,48

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

%C For a guide to related sequences, see A204892.

%e The triangular numbers: s(k)=k(k+1)/2.

%e Their differences, ordered as in A193974:

%e u(1)=s(2)-s(1)=2

%e u(2)=s(3)-s(1)=5

%e u(3)=s(3)-s(2)=3

%e u(4)=s(4)-s(1)=9

%e u(5)=s(4)-s(2)=7

%e u(6)=s(4)-s(3)=4.

%e a(1)=1 because 1 divides u(1)

%e a(2)=1 because 2 divides u(1)

%e a(3)=3 because 3 divides u(3)

%e a(4)=6 because 4 divides u(6)

%e a(5)=2 because 5 divides u(2)

%e a(6)=8 because 6 divides u(8)

%t (See the program at A205002.)

%Y Cf. A205002, A204892.

%K nonn

%O 1,3

%A _Clark Kimberling_, Jan 21 2012