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A349707 Numbers that are congruent to {0, 1, 4, 6, 8, 10, 11} (mod 12). 0
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 (list; graph; refs; listen; history; text; internal format)
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
Wikipedia, Enigmatic scale.
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
KEYWORD
nonn,easy
AUTHOR
Roberto Bertocco, Nov 26 2021
STATUS
approved

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Last modified May 26 16:43 EDT 2024. Contains 372840 sequences. (Running on oeis4.)