OFFSET
1,2
COMMENTS
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).
Positive numbers not of the form 5x + 7y with nonnegative x and y.
LINKS
Gianni A. Sarcone and Marie-Jo Waeber, Can you count in 'ding-bong'?.
EXAMPLE
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!
MATHEMATICA
Position[Table[FrobeniusSolve[{5, 7}, n], {n, 23}]/.{}->r, r]//Flatten (* Harvey P. Dale, Mar 06 2019 *)
CROSSREFS
KEYWORD
easy,fini,full,nonn
AUTHOR
Alexandre Wajnberg, Feb 04 2005
EXTENSIONS
Corrected by Zak Seidov, Oct 22 2011
Entry revised by N. J. A. Sloane, Mar 06 2019
STATUS
approved