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

1,6

Comments

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

Links

Pontus von Brömssen, Table of n, a(n) for n = 1..10000

Wikipedia, Coin problem.

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.

Example

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.

Crossrefs

Cf. A004767, A065003, A326674.

Sequence in context: A102259 A021200 A265301 * A019904 A002068 A021666

Adjacent sequences: A380693 A380694 A380695 * A380698 A380699 A380700

Keyword

nonn,new

Author

Pontus von Brömssen, Jan 30 2025

Status

approved