

A323822


Lexicographically first sequence starting with a(1) = 11, with no duplicate term, such that a(n) is the result of a selfadditive linear combination of a(n+1)'s digits (concatenated sometimes into substrings).


3



11, 29, 13, 14, 23, 17, 32, 67, 37, 34, 27, 33, 38, 24, 25, 53, 76, 48, 44, 47, 35, 54, 66, 56, 46, 45, 55, 65, 57, 36, 63, 69, 73, 78, 28, 62, 87, 39, 43, 49, 15, 52, 86, 75, 58, 26, 72, 88, 74, 68, 64, 84, 77, 83, 79, 18, 22, 92, 101, 191, 596, 460, 100, 102, 96, 213, 98, 210, 103, 131, 383, 174, 235, 305, 97, 310, 104, 221, 169, 117
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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

JeanMarc Falcoz, Table of n, a(n) for n = 1..5373


EXAMPLE

a(1) = 11 and 11 is indeed a selfadditive 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 selfadditive linear combination of the digits of a(3) = 13 as 1*2 + 1*9 = 11;
a(3) = 13 and 13 is indeed a selfadditive linear combination of the digits of a(4) = 14 as 1*1 + 3*4 = 13;
a(4) = 14 and 14 is indeed a selfadditive linear combination of the digits of a(5) = 23 as 1*2 + 4*3 = 14;
...
a(58) = 92 and 92 is indeed a selfadditive linear combination of the digits of a(59) = 101 as 9*10 + 2*1 = 92;
a(59) = 101 and 101 is indeed a selfadditive linear combination of some substrings of a(60) = 191 as 10*1 + 1*91 = 101;
a(60) = 191 and 191 is indeed a selfadditive linear combination of some substrings of a(61) = 596 as 19*5 + 1*96 = 191;
etc.


CROSSREFS

Cf. A323821 and A323823 for more sequences dealing with the idea of linear combinations.
Sequence in context: A274130 A034276 A245169 * A196357 A196360 A072711
Adjacent sequences: A323819 A323820 A323821 * A323823 A323824 A323825


KEYWORD

base,nonn


AUTHOR

Eric Angelini and JeanMarc Falcoz, Jan 30 2019


STATUS

approved



