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A190785 Numbers that are congruent to {0, 2, 3, 5, 7, 9, 11} mod 12. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified March 25 07:51 EDT 2023. Contains 361511 sequences. (Running on oeis4.)