A323821 Lexicographically first sequence starting with a(1) = 1, with no duplicate term, such that a(n) is the result of an additive linear combination of a(n+1)'s digits.

1, 10, 2, 11, 12, 3, 13, 14, 7, 15, 5, 16, 4, 17, 18, 6, 19, 21, 23, 25, 27, 9, 29, 31, 32, 8, 20, 22, 24, 26, 28, 34, 35, 37, 38, 41, 43, 45, 30, 33, 36, 39, 47, 49, 51, 52, 40, 42, 46, 53, 54, 56, 44, 48, 57, 58, 59, 61, 65, 50, 55, 67, 71, 72, 60, 62, 64, 68, 73, 74, 75, 63, 69, 76, 78, 66, 79, 81, 83, 85, 87, 89, 91, 70, 77

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

Cf. A323822 and A323823 (self-linear combinations, variant A and B).

Sequence in context: A274606 A293869 A365625 * A351840 A257277 A248024

Adjacent sequences: A323818 A323819 A323820 * A323822 A323823 A323824

Keyword

base,nonn

Author

Eric Angelini and Jean-Marc Falcoz, Jan 30 2019

Status

approved