A371902 Positive integers whose binary form follows the periodic pattern 1101110: the concatenation of halftones 2 2 1 2 2 2 1, diminished by one, between successive pitches in the Ionian Major Scale.

1, 3, 6, 13, 27, 55, 110, 221, 443, 886, 1773, 3547, 7095, 14190, 28381, 56763, 113526, 227053, 454107, 908215, 1816430, 3632861, 7265723, 14531446, 29062893, 58125787, 116251575, 232503150, 465006301, 930012603, 1860025206, 3720050413

Offset

1,2

Comments

The periodic binary digits of 55/107 is the pattern sequence A291454(n)-1 which is the new bit introduced into a(n): a(n+1) = 2*a(n) + A291454(n) - 1.

Links

Paolo Xausa, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (2,0,0,0,0,0,1,-2).

Formula

a(n) = floor((110/127)*2^n).

D.g.f.: z^2*(z^5 + z^4 + z^2 + z + 1)/((2 - z) (1 - z^7)) = z * Dgf(A000225) * Dgf(A234046).

G.f.: x*(1 + x + x^3 + x^4 + x^5)/((1 - 2*x)*(1 - x^7)). - Stefano Spezia, May 04 2024

Example

For n=10, playing 10 + 1 = 11 notes of the major scale (in Ionian mode), the 10 intervals between the pitches C D E F G A B C' D' E' F' expressed in halftones are 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, whose values diminished by one give the binary form '1101110110', which in decimal is 886, hence a(10) = 886.

Mathematica

Floor[110/127*2^Range[50]] (* Paolo Xausa, Jun 21 2024 *)

Crossrefs

Cf. A083026, A291454, A000225, A234046

Sequence in context: A055143 A092539 A094386 * A267604 A099036 A131246

Adjacent sequences: A371899 A371900 A371901 * A371903 A371904 A371905

Keyword

nonn,easy

Author

Federico Provvedi, Apr 13 2024

Status

approved