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A102701
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Non-"Ding!Bong!" numbers: positive numbers which are not a positive linear combination of 5's and 7's.
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2
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1, 2, 3, 4, 6, 8, 9, 11, 13, 16, 18, 23
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history;
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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Table of n, a(n) for n=1..12.
Gianni A. Sarcone and Marie-Jo Waeber, Can you count in 'ding-bong'?.
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EXAMPLE
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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!
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MATHEMATICA
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Position[Table[FrobeniusSolve[{5, 7}, n], {n, 23}]/.{}->r, r]//Flatten (* Harvey P. Dale, Mar 06 2019 *)
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CROSSREFS
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Cf. A000027, A102705.
Sequence in context: A341159 A214977 A135676 * A255770 A111208 A085500
Adjacent sequences: A102698 A102699 A102700 * A102702 A102703 A102704
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KEYWORD
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easy,fini,full,nonn
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AUTHOR
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Alexandre Wajnberg, Feb 04 2005
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EXTENSIONS
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Corrected by Zak Seidov, Oct 22 2011
Entry revised by N. J. A. Sloane, Mar 06 2019
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STATUS
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approved
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