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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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..12.

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

Cf. A000027, A102705.

Sequence in context: A341159 A214977 A135676 * A255770 A111208 A085500

Adjacent sequences:  A102698 A102699 A102700 * A102702 A102703 A102704

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

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Last modified April 11 08:10 EDT 2021. Contains 342886 sequences. (Running on oeis4.)