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

Author

Roberto Bertocco, Nov 26 2021

Keywords

• nonn
• easy

Comments

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

Links

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

Crossrefs

Cf. A083028.

Programs

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 *)

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

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