A190785 Numbers that are congruent to {0, 2, 3, 5, 7, 9, 11} mod 12.

0, 2, 3, 5, 7, 9, 11, 12, 14, 15, 17, 19, 21, 23, 24, 26, 27, 29, 31, 33, 35, 36, 38, 39, 41, 43, 45, 47, 48, 50, 51, 53, 55, 57, 59, 60, 62, 63, 65, 67, 69, 71, 72, 74, 75, 77, 79, 81, 83, 84, 86, 87, 89, 91, 93, 95, 96, 98, 99, 101, 103, 105, 107, 108, 110

Offset

1,2

Comments

The key-numbers of the pitches of a ascending melodic minor scale on a standard chromatic keyboard, with root = 0 and raised seventh.

First differences are period 7: repeat [1,2,2,2,2,1,2]. - Bruno Berselli, May 27 2011

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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.: ( 2+x+2*x^2+2*x^3+2*x^4+2*x^5+x^6 ) / ( (x^6+x^5+x^4+x^3+x^2+x+1)*(x-1)^2 ). - R. J. Mathar, May 26 2011

a(n) = 2*n-floor(2*n/7)-floor(((n-4) mod 7)/5). - Rolf Pleisch, Jun 11 2011

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

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

a(n) = (84*n - 77 - 2*(n mod 7) - 2*((n+1) mod 7) - 2*((n+2) mod 7) - 2*((n+3) mod 7) + 5*((n+4) mod 7) - 2*((n+5) mod 7) + 5*((n+6) mod 7))/49.

a(7*k) = 12*k-1, a(7*k-1) = 12*k-3, a(7*k-2) = 12*k-5, a(7*k-3) = 12*k-7, a(7*k-4) = 12*k-9, a(7*k-5) = 12*k-10, a(7*k-6) = 12*k-12. (End)

Maple

A190785:=n->12*floor(n/7)+[0, 2, 3, 5, 7, 9, 11][(n mod 7)+1]: seq(A190785(n), n=0..100); # Wesley Ivan Hurt, Jul 21 2016

Mathematica

Union[Flatten[Table[12n + {0, 2, 3, 5, 7, 9, 11}, {n, 0, 8}]]] (* Alonso del Arte, Jun 11 2011 *)

Prog

(Magma) [n: n in [0..110] | n mod 12 in [0, 2, 3, 5, 7, 9, 11]]; // Bruno Berselli, May 27 2011
(PARI) a(n)=n\7*12+[0, 2, 3, 5, 7, 9, 11][n%7+1] \\ Charles R Greathouse IV, Jun 08 2011
(Python)
def A190785(n):
    a, b = divmod(n-1, 7)
    return (0, 2, 3, 5, 7, 9, 11)[b]+12*a # Chai Wah Wu, Jan 26 2023

Crossrefs

Cf. A083028.

Sequence in context: A073040 A087268 A106765 * A186290 A061979 A050748

Adjacent sequences: A190782 A190783 A190784 * A190786 A190787 A190788

Keyword

nonn,easy

Author

Roberto Bertocco, May 26 2011

Extensions

Zero prepended by Wesley Ivan Hurt, Jul 21 2016

Status

approved