A175884 Numbers that are congruent to {0, 2, 4, 7, 9} mod 12.

0, 2, 4, 7, 9, 12, 14, 16, 19, 21, 24, 26, 28, 31, 33, 36, 38, 40, 43, 45, 48, 50, 52, 55, 57, 60, 62, 64, 67, 69, 72, 74, 76, 79, 81, 84, 86, 88, 91, 93, 96, 98, 100, 103, 105, 108, 110, 112, 115, 117, 120, 122, 124, 127, 129, 132, 134, 136, 139, 141, 144, 146, 148, 151

Offset: 1

Author

Bill Shillito (DMAshura(AT)gmail.com), Oct 08 2010

Keywords

• nonn
• easy

Comments

Key-numbers of the pitches of a major pentatonic scale on a standard chromatic keyboard, with root = 0.

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

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Vincenzo Librandi)
• Wikipedia, Major pentatonic scale
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,-1).

Crossrefs

Cf. A005843, A057354, A002266.

Subset of A083026 with exact index A032796.

Programs

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

Magma

[Floor(12*(n-1)/5): n in [1..100]]; // G. C. Greubel, Oct 23 2018

Maple

seq(floor(12*(n-1)/5),n=1..65); # Muniru A Asiru, Oct 24 2018

Mathematica

fQ[n_] := MemberQ[{0, 2, 4, 7, 9}, Mod[n, 12]]; Select[ Range[0, 152], fQ] (* Robert G. Wilson v, Oct 09 2010 *)
Table[2n-1+Floor[(n-4)/5]+Floor[(n-1)/5],{n, 100}] (* Federico Provvedi, Jan 13 2018 *)
Quotient[12(Range[100]-1), 5] (* Federico Provvedi, Oct 19 2018 *)

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

PARI

vector(100, n, floor(12*(n-1)/5)) \\ G. C. Greubel, Oct 23 2018

Formula

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

a(n) = 2*n - 1 + floor((n-4)/5) + floor((n-1)/5). - Federico Provvedi, Jan 13 2018

a(n) = floor(12*(n-1)/5). - Federico Provvedi, Oct 19 2018

a(n) = A005843(n) + A057354(n). - Federico Provvedi, Sep 10 2022

Extensions

Offset change by G. C. Greubel, Oct 23 2018