A380697 Frobenius number of the set S = {e_i+2; 1 <= i <= m}, where the e_i are the exponents in the binary expansion n = Sum_{i=1..m} 2^e_i, or 0 if GCD(S) = A326674(2*n) > 1.

0, 0, 1, 0, 0, 5, 1, 0, 3, 7, 1, 11, 3, 2, 1, 0, 0, 0, 1, 0, 0, 5, 1, 19, 3, 7, 1, 7, 3, 2, 1, 0, 5, 11, 1, 17, 5, 5, 1, 23, 3, 4, 1, 6, 3, 2, 1, 29, 5, 11, 1, 9, 5, 5, 1, 9, 3, 4, 1, 3, 3, 2, 1, 0, 0, 13, 1, 0, 0, 5, 1, 27, 3, 7, 1, 11, 3, 2, 1, 0, 0, 13, 1

Offset: 1

Author

Pontus von Brömssen, Jan 30 2025

Keywords

• nonn

Comments

The sequence gives the Frobenius numbers of all sets of integers greater than 1, encoded by the binary expansion of n.

Examples

			For n = 262288 = 2^4+2^7+2^18, a(n) is the Frobenius number of {6, 9, 20}, i.e., the last term of A065003, so a(262288) = 43.
		

Links

• Pontus von Brömssen, Table of n, a(n) for n = 1..10000
• Wikipedia, Coin problem.

Crossrefs

Cf. A004767, A065003, A326674.

Formula

a(n) = 1 if and only if n == 3 (mod 4) (i.e., if and only if n is in A004767).

a(n) = 2 if and only if n == 14 (mod 16).

a(2^e+2^f) = (e+1)*(f+1)-1 for nonnegative integers e and f such that e+2 and f+2 are coprime.