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A359274

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.

1, 4, 7, 10, 16, 19, 22, 25, 31, 40, 46, 49, 64, 70, 79, 94, 109, 121, 124, 139, 145, 154, 169, 184, 193, 217, 241, 265, 274, 289, 304, 313, 316, 319, 334, 337, 364, 367, 379, 391, 436, 439, 454, 460, 469, 481, 484, 499, 505, 508, 511, 556, 586, 589, 631, 634

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OFFSET

1,2

COMMENTS

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).

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.

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

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, C++ program

Index entries for sequences generated by sieves

EXAMPLE

For n = 1:

- we choose a(1) = 1,

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

For n = 2:

- we choose a(2) = 4,

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