A359274 - OEIS

%I #40 Feb 02 2023 14:44:48

%S 1,4,7,10,16,19,22,25,31,40,46,49,64,70,79,94,109,121,124,139,145,154,

%T 169,184,193,217,241,265,274,289,304,313,316,319,334,337,364,367,379,

%U 391,436,439,454,460,469,481,484,499,505,508,511,556,586,589,631,634

%N Lexicographically earliest sequence of distinct positive integers such that no term belongs to a Fibonacci-like sequence beginning with two (not necessarily distinct) smaller terms.

%C A Fibonacci-like sequence, say f, satisfies f(k) = f(k-1) + f(k-2) for any k > 1, and is uniquely determined by its two initial terms f(0) and f(1).

%C Each time a term, say a(n), is chosen, we sieve out values appearing in Fibonacci-like sequences with initial terms a(n) and a(m) (in any order) for m = 1..n.

%C The initial value a(1) = 1 is the only Fibonacci number in this sequence.

%H Rémy Sigrist, <a href="/A359274/b359274.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A359274/a359274.txt">C++ program</a>

%H <a href="/index/Si#sieve">Index entries for sequences generated by sieves</a>

%e For n = 1:

%e - we choose a(1) = 1,

%e - we sieve out the values a(1) = 1, a(1) = 1, 2, 3, 5, 8, 13, ...

%e For n = 2:

%e - we choose a(2) = 4,

%e - we sieve out the values a(1) = 1, a(2) = 4, 5, 9, 14, 23, 37, ...

%e - we sieve out the values a(2) = 4, a(2) = 4, 8, 12, 20, 32, 52, ...

%e - we sieve out the values a(2) = 4, a(1) = 1, 5, 6, 11, 17, 28, ...

%e For n = 3:

%e - we choose a(3) = 7,

%e - we sieve out the values a(1) = 1, a(3) = 7, 8, 15, 23, 38, 61, ...

%e - we sieve out the values a(2) = 4, a(3) = 7, 11, 18, 29, 47, 76, ...

%e - we sieve out the values a(3) = 7, a(3) = 7, 14, 21, 35, 56, 91, ...

%e - we sieve out the values a(3) = 7, a(2) = 4, 11, 15, 26, 41, 67, ...

%e - we sieve out the values a(3) = 7, a(1) = 1, 8, 9, 17, 26, 43, ...

%e For n = 4:

%e - we choose a(4) = 10.

%o (C++) See Links section.

%Y Cf. A000045.

%K nonn

%O 1,2

%A _Rémy Sigrist_, Jan 31 2023