Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #19 Mar 06 2019 19:35:15
%S 1,2,3,4,6,8,9,11,13,16,18,23
%N Non-"Ding!Bong!" numbers: positive numbers which are not a positive linear combination of 5's and 7's.
%C From the "Ding!Bong!" game: list the natural numbers replacing 5 by Ding! and 7 by Bong! All numbers except those listed in the sequence are combinations of Dings or of Bongs (this includes all numbers >23).
%C Positive numbers not of the form 5x + 7y with nonnegative x and y.
%H Gianni A. Sarcone and Marie-Jo Waeber, <a href="http://www.archimedes-lab.org/numbers/Num1_69.html#dingbong">Can you count in 'ding-bong'?</a>.
%e 1 2 3 4 Ding! 6 Bong! 8 9 Ding-Ding! 11 Ding-Bong! 13 Bong-Bong! Ding-Ding-Ding! 16 Ding-Ding-Bong! 18 Ding-Bong-Bong! Ding-Ding-Ding-Ding! Bong-Bong-Bong! Ding-Ding-Ding-Bong! 23 Ding-Ding-Bong-Bong! Ding-Ding-Ding-Ding-Ding! Ding-Bong-Bong-Bong! Ding-Ding-Ding-Ding-Bong! Bong-Bong-Bong-Bong! Ding-Ding-Ding-Bong-Bong! Ding-Ding-Ding-Ding-Ding-Ding!
%t Position[Table[FrobeniusSolve[{5,7},n],{n,23}]/.{}->r,r]//Flatten (* _Harvey P. Dale_, Mar 06 2019 *)
%Y Cf. A000027, A102705.
%K easy,fini,full,nonn
%O 1,2
%A _Alexandre Wajnberg_, Feb 04 2005
%E Corrected by _Zak Seidov_, Oct 22 2011
%E Entry revised by _N. J. A. Sloane_, Mar 06 2019