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Absolute difference of final digits of two consecutive triangular numbers.
1

%I #16 Dec 14 2023 05:24:48

%S 1,2,3,6,5,4,7,2,1,0,1,2,7,4,5,6,3,2,1,0,1,2,3,6,5,4,7,2,1,0,1,2,7,4,

%T 5,6,3,2,1,0,1,2,3,6,5,4,7,2,1,0,1,2,7,4,5,6,3,2,1,0,1,2,3,6,5,4,7,2,

%U 1,0,1,2,7,4,5,6,3,2,1,0,1,2,3,6,5,4,7,2,1,0,1,2,7,4,5,6,3,2,1,0,1,2,3,6,5

%N Absolute difference of final digits of two consecutive triangular numbers.

%C Periodic with period 20.

%H <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).

%F a(n) = abs{ A010879[A000217(n+1)] - A010879[A000217(n)] }. - _R. J. Mathar_, Jul 15 2007

%p A000217 := proc(n) n*(n+1)/2 ; end: A010879 := proc(n) n mod 10 ; end: A130686 := proc(n) abs(A010879(A000217(n+1))-A010879(A000217(n))) ; end: seq(A130686(n),n=0..80) ; # _R. J. Mathar_, Jul 15 2007

%Y Cf. A008954.

%K base,easy,nonn

%O 1,2

%A _Giovanni Teofilatto_, Jun 30 2007