A349707 Numbers that are congruent to {0, 1, 4, 6, 8, 10, 11} (mod 12).

0, 1, 4, 6, 8, 10, 11, 12, 13, 16, 18, 20, 22, 23, 24, 25, 28, 30, 32, 34, 35, 36, 37, 40, 42, 44, 46, 47, 48, 49, 52, 54, 56, 58, 59, 60, 61, 64, 66, 68, 70, 71, 72, 73, 76, 78, 80, 82, 83, 84, 85, 88, 90, 92, 94, 95, 96, 97, 100, 102, 104, 106, 107, 108, 109

Offset

1,3

Comments

Terms are the key numbers of the pitches of an Enigmatic scale on a standard chromatic keyboard, with root = 0.

Links

Table of n, a(n) for n=1..65.

Wikipedia, Enigmatic scale.

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

Formula

G.f.: x^2*(1 + 3*x + 2*x^2 + 2*x^3 + 2*x^4 + x^5 + x^6)/((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)). - Stefano Spezia, Dec 01 2021

a(n) = a(n-7) + 12 for n >= 8. - Michael S. Branicky, Dec 02 2021

Mathematica

upto=200; Select[Range[0, upto], MemberQ[{0, 1, 4, 6, 8, 10, 11}, Mod[#, 12]]&] (* Paolo Xausa, Nov 30 2021 *)
nterms=100; LinearRecurrence[{1, 0, 0, 0, 0, 0, 1, -1}, {0, 1, 4, 6, 8, 10, 11, 12}, nterms] (* Paolo Xausa, Nov 30 2021 *)

Prog

(Python)
def a(n): return 12*((n-1)//7) + [0, 1, 4, 6, 8, 10, 11][(n-1)%7]
print([a(n) for n in range(1, 66)]) # Michael S. Branicky, Dec 02 2021

Crossrefs

Cf. A083028.

Sequence in context: A020891 A340848 A090967 * A272475 A184016 A075254

Adjacent sequences: A349704 A349705 A349706 * A349708 A349709 A349710

Keyword

nonn,easy

Author

Roberto Bertocco, Nov 26 2021

Status

approved