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A214777 McNugget numbers: numbers of the form 6*x + 9*y + 20*z for nonnegative integers x, y, z.

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%I A214777 #34 Feb 24 2025 14:38:53
%S A214777 0,6,9,12,15,18,20,21,24,26,27,29,30,32,33,35,36,38,39,40,41,42,44,45,
%T A214777 46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,
%U A214777 69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86
%N A214777 McNugget numbers: numbers of the form 6*x + 9*y + 20*z for nonnegative integers x, y, z.
%C A214777 A214772(a(n)) > 0;
%C A214777 complement of A065003; all numbers greater than 43 are McNugget numbers: Frobenius(6,9,20) = 43.
%H A214777 Reinhard Zumkeller, <a href="/A214777/b214777.txt">Table of n, a(n) for n = 1..1000</a>
%H A214777 Scott Chapman, Christopher O'Neill, <a href="https://arxiv.org/abs/1709.01606">Factoring in the Chicken McNugget monoid</a>, arXiv:1709.01606 [math.AC], 2017.
%H A214777 Anita Wah and Henri Picciotto, <a href="http://www.mathedpage.org/attc/lessons/ch.05/5.08-building-blocks.pdf">Lesson in Algebra: Themes, Tools, Concepts</a>
%H A214777 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FrobeniusNumber.html">Frobenius Number</a>.
%H A214777 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/McNuggetNumber.html">McNugget Numbers</a>.
%H A214777 Wikipedia, <a href="http://en.wikipedia.org/wiki/Coin_problem">Coin problem</a>
%H A214777 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A214777 G.f.: -x^2*(x^22-x^21+x^17-x^16+x^15-x^14+x^13-x^12+x^11-x^10+x^9+x^8-2*x^7+x^6+x^5+3*x-6) / (x-1)^2. - _Colin Barker_, Dec 13 2012
%F A214777 a(n) = n + 21 for n >= 23. - _Robert Israel_, May 01 2015
%t A214777 CoefficientList[Series[- x (x^22 - x^21 + x^17 - x^16 + x^15 - x^14 + x^13 - x^12 + x^11 - x^10 + x^9 + x^8 - 2 x^7 + x^6 + x^5 + 3 x - 6)/(1 - x)^2, {x, 0, 70}], x] (* _Vincenzo Librandi_, Apr 27 2015 *)
%o A214777 (Haskell)
%o A214777 import Data.List (findIndices)
%o A214777 a214777 n = a214777_list !! (n-1)
%o A214777 a214777_list = findIndices (> 0) a214772_list
%o A214777 (Python)
%o A214777 def A214777(n): return (0, 6, 9, 12, 15, 18, 20, 21, 24, 26, 27, 29, 30, 32, 33, 35, 36, 38, 39, 40, 41, 42)[n-1] if n<23 else n+21 # _Chai Wah Wu_, Feb 24 2025
%Y A214777 Cf. A065003, A214772.
%K A214777 nonn,easy
%O A214777 1,2
%A A214777 _Reinhard Zumkeller_, Jul 28 2012