OFFSET
1,2
FORMULA
Conjectures from Colin Barker, Apr 09 2020: (Start)
G.f.: x*(1 + 2*x + x^2 - x^4 - 2*x^5 - 4*x^7) / (1 - 2*x^2).
a(n) = 2*a(n-2) for n>6.
(End)
Conjecture: a(n) = 2^((n-7)/2)*(5 + 2*sqrt(2) + (2*sqrt(2) - 5)*(-1)^n) for n > 6. - Stefano Spezia, Oct 23 2021
EXAMPLE
a(1) = 1 divides 23 (and 23 is a(2) = 2 concatenated to a(3) = 3);
a(2) = 2 divides 34 (and 34 is a(3) = 3 concatenated to a(4) = 4);
a(3) = 3 divides 45 (and 45 is a(4) = 4 concatenated to a(5) = 5);
a(4) = 4 divides 56 (and 56 is a(5) = 5 concatenated to a(6) = 6);
a(5) = 5 divides 610 (and 610 is a(6) = 6 concatenated to a(7) = 10);
a(6) = 6 divides 108 (and 108 is a(7) = 10 concatenated to a(8) = 8);
From a(7) = 10 on, the pattern of the sequence is regular.
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Eric Angelini, Apr 09 2020
STATUS
approved