A032796 Numbers that are congruent to {1, 2, 3, 5, 6} mod 7.
1, 2, 3, 5, 6, 8, 9, 10, 12, 13, 15, 16, 17, 19, 20, 22, 23, 24, 26, 27, 29, 30, 31, 33, 34, 36, 37, 38, 40, 41, 43, 44, 45, 47, 48, 50, 51, 52, 54, 55, 57, 58, 59, 61, 62, 64, 65, 66, 68, 69, 71, 72, 73, 75, 76, 78, 79, 80, 82, 83, 85, 86, 87, 89, 90, 92, 93, 94, 96, 97, 99
Offset: 1
Links
- Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,-1).
Programs
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Magma
[n: n in [0..120] | n mod 7 in {1, 2, 3, 5, 6}]; // Vincenzo Librandi, Dec 29 2010 -
Mathematica
#+{1,2,3,5,6}&/@(7*Range[0,15])//Flatten (* or *) LinearRecurrence[ {1,0,0,0,1,-1},{1,2,3,5,6,8},100] (* Harvey P. Dale, Oct 07 2018 *)
Formula
Equals natural numbers minus '4, 7, 11, 14, 18, ...' (= previous term +3, +4, +3, +4, ...).
G.f.: x*(x^5 + x^4 + 2*x^3 + x^2 + x + 1)/((1-x)*(1-x^5)).
a(n) = (m^3 - 6*m^2 + 17*m + 6*(7*floor(n/5)-1))/6, where m = n mod 5. - Luce ETIENNE,Oct 17 2018
Comments