login
A102701
Non-"Ding!Bong!" numbers: positive numbers which are not a positive linear combination of 5's and 7's.
2
1, 2, 3, 4, 6, 8, 9, 11, 13, 16, 18, 23
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
Sequence in context: A374177 A214977 A135676 * A255770 A348196 A111208
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