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

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, ...
- we sieve out the values a(2) = 4, a(2) = 4, 8, 12, 20, 32, 52, ...
- we sieve out the values a(2) = 4, a(1) = 1, 5, 6, 11, 17, 28, ...
For n = 3:
- we choose a(3) = 7,
- we sieve out the values a(1) = 1, a(3) = 7, 8, 15, 23, 38, 61, ...
- we sieve out the values a(2) = 4, a(3) = 7, 11, 18, 29, 47, 76, ...
- we sieve out the values a(3) = 7, a(3) = 7, 14, 21, 35, 56, 91, ...
- we sieve out the values a(3) = 7, a(2) = 4, 11, 15, 26, 41, 67, ...
- we sieve out the values a(3) = 7, a(1) = 1, 8, 9, 17, 26, 43, ...
For n = 4:
- we choose a(4) = 10.

Prog

(C++) See Links section.

Crossrefs

Cf. A000045.

Sequence in context: A310709 A310710 A138694 * A177965 A179209 A168565

Adjacent sequences: A359271 A359272 A359273 * A359275 A359276 A359277

Keyword

nonn

Author

Rémy Sigrist, Jan 31 2023

Status

approved