A298306 The Frobenius number of the set of binary n-th powers, divided out by its GCD.

17, 723, 52753, 49790415, 126629

Offset

2,1

Comments

The binary n-th powers are those positive integers whose base-2 representation consists of n consecutive identical blocks. For example, the binary squares 3, 10, 15, ... form sequence A020330. The GCD of the binary n-th powers form sequence A014491. The Frobenius number of a set S with GCD 1 is the largest number not representable as an N-linear combination of members of S.

Links

Table of n, a(n) for n=2..6.

Daniel M. Kane, Carlo Sanna, and Jeffrey Shallit, Waring's theorem for binary powers, arXiv:1801.04483 [math.NT], Jan 13 2018.

Example

For n = 2 the first few binary squares are 3, 10, 15, 36, ... with GCD 1 and the Frobenius number of (3, 10, 15, 36) is 17.

Crossrefs

Cf. A020330, A014491.

Sequence in context: A012193 A128274 A012085 * A308696 A308594 A308570

Adjacent sequences: A298303 A298304 A298305 * A298307 A298308 A298309

Keyword

nonn,more

Author

Jeffrey Shallit, Jan 16 2018

Status

approved