OFFSET
1,2
COMMENTS
Conjecture. For any positive integer a(1), the sequence generated according to the above rule eventually cycles through the forms a(k)=[1][4^a][3][(84)^b],..., a(k+6)=[1][4^a][3][(84)^(b+1)], or through a(k)=[1][5^a][4][(84)^b],..., a(k+6)=[1][5^a][4][(84)^(b+1)], for nonnegative integers a and b. The sequence listed above, with a(1)=1, is an example of the first type.
FORMULA
Conjectures from Colin Barker, Feb 15 2016: (Start)
a(n) = a(n-2) + 10*a(n-3) - 10*a(n-5) for n>7.
G.f.: x*(1+2*x+7*x^2+2*x^3-x^4+10*x^5-10*x^6+10*x^8) / ((1-x)*(1+x)*(1-10*x^3)). (End)
From Robert Israel, Feb 15 2016: (Start)
For k >= 1:
a(6*k-4) = 2*10^(2*k-2) + 84*(10^(2*k-2)-1)/99.
a(6*k-3) = 94*10^(2*k-3) + 84*(10^(2*k-3)-10)/99 + 7.
a(6*k-2) = 13*10^(2*k-2) + 84*(10^(2*k-2)-1)/99.
a(6*k-1) = 2*10^(2*k-1) + 84*(10^(2*k-1)-10)/99 + 7.
a(6*k) = 94*10^(2*k-2) + 84*(10^(2*k-2)-1)/99.
a(6*k+1) = 13*10^(2*k-1) + 84*(10^(2*k-1)-10)/99 + 7.
Colin Barker's conjectures follow from these. (End)
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
John W. Layman, Feb 14 2000
STATUS
approved