OFFSET
1,1
COMMENTS
A linear combination is an operation like a*u + b*v + c*w + d*x + ... = N. [We want only (+) signs here, thus the word "additive" in the definition.] The coefficients a, b, c, d, ... are not free (as opposed to the sequence visible in A323821): they are determined by the digits of a(n) itself; u, v, w, x, ... are determined by the digits of a(n+1) [up to a(58): from a(59) = 101 on, the quantities involved in the linear combination might be substrings of either a(n) or a(n+1), or both (no substring with a leading zero is allowed)].
This sequence is not a permutation of the positive integers > 10 as 99 will never appear (at the moment 99 appears, there are no more available successors).
LINKS
Jean-Marc Falcoz, Table of n, a(n) for n = 1..5373
EXAMPLE
a(1) = 11 and 11 is indeed a self-additive linear combination of the digits of a(2) = 29 as 1*2 + 1*9 = 11 (29 being among others like 38, 47, 56, 65, ... the smallest available integer with this property). Note that, in the examples here, the digits before the (*) sign rebuild, in their original order, the integer a(n) and the digits after the (*) sign rebuild, in their original order, the integer a(n+1);
a(2) = 29 and 29 is indeed a self-additive linear combination of the digits of a(3) = 13 as 1*2 + 1*9 = 11;
a(3) = 13 and 13 is indeed a self-additive linear combination of the digits of a(4) = 14 as 1*1 + 3*4 = 13;
a(4) = 14 and 14 is indeed a self-additive linear combination of the digits of a(5) = 23 as 1*2 + 4*3 = 14;
...
a(58) = 92 and 92 is indeed a self-additive linear combination of the digits of a(59) = 101 as 9*10 + 2*1 = 92;
a(59) = 101 and 101 is indeed a self-additive linear combination of some substrings of a(60) = 191 as 10*1 + 1*91 = 101;
a(60) = 191 and 191 is indeed a self-additive linear combination of some substrings of a(61) = 596 as 19*5 + 1*96 = 191;
etc.
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Eric Angelini and Jean-Marc Falcoz, Jan 30 2019
STATUS
approved