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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
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.
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
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Jan 31 2023
STATUS
approved