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

0, 6, 9, 12, 15, 18, 20, 21, 24, 26, 27, 29, 30, 32, 33, 35, 36, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86

Offset: 1

Author

Reinhard Zumkeller, Jul 28 2012

Keywords

• nonn
• easy

Comments

A214772(a(n)) > 0;

complement of A065003; all numbers greater than 43 are McNugget numbers: Frobenius(6,9,20) = 43.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
• Scott Chapman, Christopher O'Neill, Factoring in the Chicken McNugget monoid, arXiv:1709.01606 [math.AC], 2017.
• Anita Wah and Henri Picciotto, Lesson in Algebra: Themes, Tools, Concepts
• Eric Weisstein's World of Mathematics, Frobenius Number.
• Eric Weisstein's World of Mathematics, McNugget Numbers.
• Wikipedia, Coin problem
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A065003, A214772.

Programs

Haskell

import Data.List (findIndices)
a214777 n = a214777_list !! (n-1)
a214777_list = findIndices (> 0) a214772_list

Mathematica

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 *)

Python

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

Formula

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

a(n) = n + 21 for n >= 23. - Robert Israel, May 01 2015