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A323822 Lexicographically first sequence starting with a(1) = 11, with no duplicate term, such that a(n) is the result of a self-additive linear combination of a(n+1)'s digits (concatenated sometimes into substrings). 3

%I

%S 11,29,13,14,23,17,32,67,37,34,27,33,38,24,25,53,76,48,44,47,35,54,66,

%T 56,46,45,55,65,57,36,63,69,73,78,28,62,87,39,43,49,15,52,86,75,58,26,

%U 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

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

%C 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)].

%C 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).

%H Jean-Marc Falcoz, <a href="/A323822/b323822.txt">Table of n, a(n) for n = 1..5373</a>

%e 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);

%e 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;

%e 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;

%e 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;

%e ...

%e 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;

%e 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;

%e 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;

%e etc.

%Y Cf. A323821 and A323823 for more sequences dealing with the idea of linear combinations.

%K base,nonn

%O 1,1

%A _Eric Angelini_ and _Jean-Marc Falcoz_, Jan 30 2019

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Last modified January 25 21:23 EST 2021. Contains 340427 sequences. (Running on oeis4.)