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

17, 723, 52753, 49790415, 126629

Offset: 2

Author

Jeffrey Shallit, Jan 16 2018

Keywords

• nonn
• more

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A020330, A014491.