

A323823


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


3



1, 100, 101, 143, 182, 273, 364, 429, 455, 546, 637, 693, 728, 819, 924, 1010, 1020, 1030, 1040, 1050, 1060, 1070, 1080, 1090, 1233, 1370, 1371, 3288, 8833, 10000, 10001, 10100, 10110, 10120, 10130, 10140, 10150, 10160, 10170, 10180, 10190, 10200, 10210, 10220, 10230, 10240, 10250, 10260, 10270, 10280, 10290, 10300, 10310, 10320
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OFFSET

1,2


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,... and u, v, w, x,... are determined by the digits of a(n) itself, concatenated sometimes into substrings (no substring with a leading zero is allowed). No digit belongs to more than one substring and all digits are involved in the linear combination.
Some patterns are distinguishable:
a(1067) = 138614  13 86 14
a(1068) = 148515  14 85 15
a(1069) = 158416  15 84 16
a(1070) = 168317  16 83 17
a(1071) = 178218  17 82 18
a(1072) = 188119  18 81 19
a(1073) = 198020  19 80 20
a(1074) = 207921  20 79 21
a(1075) = 217822  21 78 22
[pattern stops there]


LINKS

JeanMarc Falcoz, Table of n, a(n) for n = 1..1165


EXAMPLE

a(1) = 1 belongs to the sequence as 1 = 1*1 [the digits appearing to the left of the (*) sign rebuild a(n); the same is true with the digits appearing to the right of the (*) sign];
10 does not belong to the sequence as 10 = 10*1 + 0*0, although being true, involves 5 digits instead of 4;
36 does not belong to the sequence as 36 = 3*6 + 6*3, although being true and involving 4 digits, doesn't respect the order in which the digits should appear in the linear combination;
a(2) = 100 belongs to the sequence as 100 = 10*10 + 0*0;
a(3) = 101 belongs to the sequence as 101 = 10*10 + 1*1;
a(4) = 143 belongs to the sequence as 143 = 14*1 + 3*43;
a(5) = 182 belongs to the sequence as 182 = 18*1 + 2*82;
etc.


CROSSREFS

Cf. A323821 and A323822 for sequences dealing with the same idea of linear combination.
Sequence in context: A280825 A233345 A091254 * A085251 A178530 A063010
Adjacent sequences: A323820 A323821 A323822 * A323824 A323825 A323826


KEYWORD

base,nonn


AUTHOR

Eric Angelini and JeanMarc Falcoz, Jan 30 2019


STATUS

approved



