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A342581
Frobenius number of the evil numbers (A001969) starting with the n-th term.
1
7, 13, 14, 16, 31, 31, 31, 32, 55, 55, 55, 55, 55, 61, 62, 64, 69, 74, 81, 127, 127, 127, 127, 127, 127, 127, 127, 127, 127, 127, 127, 128, 133, 138, 145, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223
OFFSET
3,1
COMMENTS
The Frobenius number of a set S is the largest positive integer t such that t cannot be written as a nonnegative integer linear combination of the elements of S.
This sequence is 2-synchronized; there is a deterministic finite automaton accepting both n and a(n) in parallel, expressed in base 2. From this, values of the sequence at certain special values (e.g., powers of 2) are easily computed.
LINKS
Jeffrey Shallit, Frobenius numbers and automatic sequences, arXiv:2103.10904 [math.NT], 2021.
EXAMPLE
For n = 4, the Frobenius number of (5, 6, 9, 10, 12, 15, ...) is 13.
CROSSREFS
Cf. A001969. The analogous sequence for the odious numbers is A342579.
Sequence in context: A376298 A057930 A363491 * A353443 A332480 A233593
KEYWORD
nonn,base
AUTHOR
Jeffrey Shallit, Mar 15 2021
STATUS
approved