A190719 Numbers that are congruent to {0, 1, 3, 5, 7, 8, 11} mod 12.

0, 1, 3, 5, 7, 8, 11, 12, 13, 15, 17, 19, 20, 23, 24, 25, 27, 29, 31, 32, 35, 36, 37, 39, 41, 43, 44, 47, 48, 49, 51, 53, 55, 56, 59, 60, 61, 63, 65, 67, 68, 71, 72, 73, 75, 77, 79, 80, 83, 84, 85, 87, 89, 91, 92, 95, 96, 97, 99, 101, 103, 104, 107, 108, 109, 111

Offset

1,3

Comments

The key-numbers of the pitches of a minor neapolitan scale on a standard chromatic keyboard, with root = 0.

This sequence contains all odd primes. - Jonathan Vos Post, Jun 09 2011

Links

Table of n, a(n) for n=1..66.

Wikipedia, Neapolitan scale

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,1,-1).

Formula

a(n) = a(n-1) + a(n-7) - a(n-8) for n>8.

G.f.: x^2*(1+2*x+2*x^2+2*x^3+x^4+3*x^5+x^6) / ( (x^6+x^5+x^4+x^3+x^2+x+1)*(x-1)^2 ). - R. J. Mathar, Jun 11 2011

a(n) = floor(12*n/7) - floor((n mod 7)/6) - floor(((n+3) mod 7)/5). - Rolf Pleisch, Jun 12 2011

From Wesley Ivan Hurt, Jul 21 2016: (Start)

a(n) = a(n-7) + 12 for n>7.

a(n) = (84*n - 91 - 9*(n mod 7) + 5*((n+1) mod 7) - 2*((n+2) mod 7) - 2*((n+3) mod 7) - 2*((n+4) mod 7) + 5*((n+5) mod 7) + 5*((n+6) mod 7))/49.

a(7k) = 12k-1, a(7k-1) = 12k-4, a(7k-2) = 12k-5, a(7k-3) = 12k-7, a(7k-4) = 12k-9, a(7k-5) = 12k-11, a(7k-6) = 12k-12. (End)

Maple

A190719:=n->12*floor(n/7)+[0, 1, 3, 5, 7, 8, 11][(n mod 7)+1]: seq(A190719(n), n=0..100); # Wesley Ivan Hurt, Jul 21 2016

Mathematica

Select[Range[0, 120], MemberQ[{0, 1, 3, 5, 7, 8, 11}, Mod[#, 12]]&] (* Harvey P. Dale, Jun 10 2011 *)

Prog

(Magma) [n : n in [0..150] | n mod 12 in [0, 1, 3, 5, 7, 8, 11]]; // Wesley Ivan Hurt, Jul 21 2016

Crossrefs

Cf. A190785.

Sequence in context: A239419 A195439 A338446 * A187224 A106252 A184415

Adjacent sequences: A190716 A190717 A190718 * A190720 A190721 A190722

Keyword

nonn,easy

Author

Roberto Bertocco, May 29 2011

Status

approved