cp's OEIS Frontend

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.

%I A380697 #13 Feb 01 2025 23:14:04
%S A380697 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,
%T A380697 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,
%U A380697 13,1,0,0,5,1,27,3,7,1,11,3,2,1,0,0,13,1
%N 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.
%C A380697 The sequence gives the Frobenius numbers of all sets of integers greater than 1, encoded by the binary expansion of n.
%H A380697 Pontus von Brömssen, <a href="/A380697/b380697.txt">Table of n, a(n) for n = 1..10000</a>
%H A380697 Wikipedia, <a href="https://en.wikipedia.org/wiki/Coin_problem">Coin problem</a>.
%F A380697 a(n) = 1 if and only if n == 3 (mod 4) (i.e., if and only if n is in A004767).
%F A380697 a(n) = 2 if and only if n == 14 (mod 16).
%F A380697 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.
%e A380697 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.
%Y A380697 Cf. A004767, A065003, A326674.
%K A380697 nonn
%O A380697 1,6
%A A380697 _Pontus von Brömssen_, Jan 30 2025