A111362 Sequence defined by an recurrence.

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, 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, 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

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

Links

Table of n, a(n) for n=1..105.

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

Sequence in context: A009492 A009810 A324156 * A134581 A099587 A172160

Adjacent sequences: A111359 A111360 A111361 * A111363 A111364 A111365

Keyword

easy,nonn

Author

Stefan Steinerberger, Nov 07 2005

Extensions

More terms from Robert G. Wilson v, Nov 09 2005

Status

approved