A111362 - OEIS

%I #12 Jul 16 2015 22:58:15

%S 1,2,3,4,4,0,3,7,8,7,6,4,0,1,9,2,9,0,0,0,9,5,2,3,0,8,8,7,5,0,7,2,6,0,

%T 9,9,8,5,6,0,6,7,9,8,7,4,6,4,3,3,8,9,8,6,0,3,5,0,1,8,8,6,1,7,8,9,4,0,

%U 8,7,3,2,1,4,0,6,9,7,4,5,0,0,4,5,7,8,5,8,8,2,5,5,2,7,6,0,4,9,3,0,1,0,6,2,9

%N Sequence defined by an recurrence.

%C In the given reference it is asked if the system of equations a(n) = 5, a(n+1)=2, a(n+2) = 1, a(n+3) = 7 can be solved. The authors negate this and also mention that a(n) = a(n+434) and so it is very easy to find a proof of the nonexistence of such solutions by using a computer.

%C Cyclic with period 434. - _Robert G. Wilson v_, Nov 09 2005

%D A. Born and G. J. Woeginger, Unerreichbare Situationen in Diskreten Systemen ("Unattainable situations in discrete systems"), Wissenschaftliche Nachrichten, Nr. 127 (2005), p. 35

%F a(1)=1, a(2)= 2, a(3)=3, a(4)=4, a(n)=5a(n-1)+3a(n-2)+2a(n-3)+a(n-4) (modulo 10).

%e a(6) = 5*a(5)+3*a(4)+2*a(3)+a(2) modulo 10 = 0

%t a[1] = 1; a[2] = 2; a[3] = 3; a[4] = 4; a[n_] := a[n] = Mod[5a[n - 1] + 3a[n - 2] + 2a[n - 3] + a[n - 4], 10]; Table[ a[n], {n, 105}] (* _Robert G. Wilson v_ *)

%K easy,nonn

%O 1,2

%A _Stefan Steinerberger_, Nov 07 2005

%E More terms from _Robert G. Wilson v_, Nov 09 2005