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A323823 Lexicographically first sequence starting with a(1) = 1, with no duplicate term, such that a(n) is the result of a self-additive 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 (list; graph; refs; listen; history; text; internal format)
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

Jean-Marc 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 Jean-Marc Falcoz, Jan 30 2019

STATUS

approved

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Last modified January 20 08:35 EST 2021. Contains 340301 sequences. (Running on oeis4.)