OFFSET
1,2
COMMENTS
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.
Cyclic with period 434. - Robert G. Wilson v, Nov 09 2005
REFERENCES
A. Born and G. J. Woeginger, Unerreichbare Situationen in Diskreten Systemen ("Unattainable situations in discrete systems"), Wissenschaftliche Nachrichten, Nr. 127 (2005), p. 35
FORMULA
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).
EXAMPLE
a(6) = 5*a(5)+3*a(4)+2*a(3)+a(2) modulo 10 = 0
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Stefan Steinerberger, Nov 07 2005
EXTENSIONS
More terms from Robert G. Wilson v, Nov 09 2005
STATUS
approved