%I #71 Oct 25 2022 20:19:01
%S 0,2,4,7,9,12,14,16,19,21,24,26,28,31,33,36,38,40,43,45,48,50,52,55,
%T 57,60,62,64,67,69,72,74,76,79,81,84,86,88,91,93,96,98,100,103,105,
%U 108,110,112,115,117,120,122,124,127,129,132,134,136,139,141,144,146,148,151
%N Numbers that are congruent to {0, 2, 4, 7, 9} mod 12.
%C Key-numbers of the pitches of a major pentatonic scale on a standard chromatic keyboard, with root = 0.
%C The pentatonic scale can also be obtained by omitting the 4th and 7th notes from the diatonic scale, so a(n) = A083026(A032796(n)). - _Federico Provvedi_, Sep 10 2022
%H G. C. Greubel, <a href="/A175884/b175884.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Vincenzo Librandi)
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Pentatonic_scale#Major_pentatonic_scale">Major pentatonic scale</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,1,-1).
%F G.f.: x^2*(2 + 2*x + 3*x^2 + 2*x^3 + 3*x^4) / ((x^4 + x^3 + x^2 + x + 1)*(x-1)^2). - _R. J. Mathar_, Jul 10 2015
%F a(n) = 2*n - 1 + floor((n-4)/5) + floor((n-1)/5). - _Federico Provvedi_, Jan 13 2018
%F a(n) = floor(12*(n-1)/5). - _Federico Provvedi_, Oct 19 2018
%F a(n) = A005843(n) + A057354(n). - _Federico Provvedi_, Sep 10 2022
%p seq(floor(12*(n-1)/5),n=1..65); # _Muniru A Asiru_, Oct 24 2018
%t fQ[n_] := MemberQ[{0, 2, 4, 7, 9}, Mod[n, 12]]; Select[ Range[0, 152], fQ] (* _Robert G. Wilson v_, Oct 09 2010 *)
%t Table[2n-1+Floor[(n-4)/5]+Floor[(n-1)/5],{n, 100}] (* _Federico Provvedi_, Jan 13 2018 *)
%t Quotient[12(Range[100]-1), 5] (* _Federico Provvedi_, Oct 19 2018 *)
%o (PARI) a(n)=([0,1,0,0,0,0; 0,0,1,0,0,0; 0,0,0,1,0,0; 0,0,0,0,1,0; 0,0,0,0,0,1; -1,1,0,0,0,1]^n*[0;2;4;7;9;12])[1,1] \\ for offset 0; _Charles R Greathouse IV_, Jul 06 2017
%o (PARI) vector(100, n, floor(12*(n-1)/5)) \\ _G. C. Greubel_, Oct 23 2018
%o (Magma) [Floor(12*(n-1)/5): n in [1..100]]; // _G. C. Greubel_, Oct 23 2018
%o (GAP) Filtered([0..151],n->n mod 12 = 0 or n mod 12 = 2 or n mod 12 = 4 or n mod 12 = 7 or n mod 12 = 9); # _Muniru A Asiru_, Oct 24 2018
%Y Cf. A005843, A057354, A002266.
%Y Subset of A083026 with exact index A032796.
%K nonn,easy
%O 1,2
%A Bill Shillito (DMAshura(AT)gmail.com), Oct 08 2010
%E Offset change by _G. C. Greubel_, Oct 23 2018