OFFSET
1,2
COMMENTS
A linear combination is an operation like a*u + b*v + c*w + d*x + ... = N. The coefficients a, b, c, d, ... are free here (although they must be >= 0, thus the word "additive" in the definition); u, v, w, x, ... are determined by the digits of a(n+1).
LINKS
Jean-Marc Falcoz, Table of n, a(n) for n = 1..2061
EXAMPLE
a(1) = 1 and this 1 is indeed an additive linear combination of the digits of 10: 1*1 + 0*0 = 1 [in the examples here, the digits after the (*) sign rebuild, in their original order, the integer a(n+1)].
a(2) = 10 as 10 is the smallest available integer leading to a(1) = 1 (as seen above).
a(3) = 2 as 2 is the smallest available integer leading to a(2) = 10: 5*2 = 10.
a(4) = 11 as 11 is the smallest available integer leading to a(3) = 2: 2*1 + 0*1 = 2.
a(5) = 12 as 12 is the smallest available integer leading to a(4) = 11: 9*1 + 1*2 = 11.
a(6) = 3 as 3 is the smallest available integer leading to a(5) = 12: 4*3 = 12.
...
a(19) = 23 as 23 is the smallest available integer leading to a(18) = 21 (7 has already been used, as all the available integers < 23): 9*2 + 1*3 = 21.
Etc.
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Eric Angelini and Jean-Marc Falcoz, Jan 30 2019
STATUS
approved