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A267747 Numbers k such that k mod 2 = k mod 3 = k mod 5. 1

%I #39 Sep 08 2022 08:46:15

%S 0,1,30,31,60,61,90,91,120,121,150,151,180,181,210,211,240,241,270,

%T 271,300,301,330,331,360,361,390,391,420,421,450,451,480,481,510,511,

%U 540,541,570,571,600,601,630,631,660,661,690,691,720,721,750,751,780,781,810,811,840

%N Numbers k such that k mod 2 = k mod 3 = k mod 5.

%C Numbers k such that k == 0 or 1 (mod 30). - _Robert Israel_, Jan 20 2016

%H Colin Barker, <a href="/A267747/b267747.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).

%F a(n) = 15*n - 7*(-1)^n - 22.

%F G.f.: x^2*(29*x+1)/((x-1)^2*(x+1)).

%t Table[15*n - 7*(-1)^n - 22, {n, 1000}] (* Or *)

%t Select[ Range[0, 20000], (Mod[#, 2]==Mod[#, 3]==Mod[#, 5]) &]

%t LinearRecurrence[{1,1,-1},{0,1,30},60] (* _Harvey P. Dale_, Nov 15 2021 *)

%o (PARI) concat(0, Vec(x^2*(29*x+1)/((x-1)^2*(x+1)) + O(x^60))) \\ _Colin Barker_, Jan 21 2016

%o (Magma) [15*n-7*(-1)^n-22: n in [1..60]]; // _Vincenzo Librandi_, Jan 21 2016

%Y Cf. A267711.

%K nonn,easy

%O 1,3

%A _Mikk Heidemaa_, Jan 20 2016

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Last modified March 29 11:14 EDT 2024. Contains 371278 sequences. (Running on oeis4.)