cp's OEIS Frontend

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.

%I A371902 #51 Jun 21 2024 16:04:03
%S A371902 1,3,6,13,27,55,110,221,443,886,1773,3547,7095,14190,28381,56763,
%T A371902 113526,227053,454107,908215,1816430,3632861,7265723,14531446,
%U A371902 29062893,58125787,116251575,232503150,465006301,930012603,1860025206,3720050413
%N 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.
%C A371902 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.
%H A371902 Paolo Xausa, <a href="/A371902/b371902.txt">Table of n, a(n) for n = 1..1000</a>
%H A371902 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,0,0,0,0,1,-2).
%F A371902 a(n) = floor((110/127)*2^n).
%F A371902 D.g.f.: z^2*(z^5 + z^4 + z^2 + z + 1)/((2 - z) (1 - z^7)) = z * Dgf(A000225) * Dgf(A234046).
%F A371902 G.f.: x*(1 + x + x^3 + x^4 + x^5)/((1 - 2*x)*(1 - x^7)). - _Stefano Spezia_, May 04 2024
%e A371902 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.
%t A371902 Floor[110/127*2^Range[50]] (* _Paolo Xausa_, Jun 21 2024 *)
%Y A371902 Cf. A083026, A291454, A000225, A234046
%K A371902 nonn,easy
%O A371902 1,2
%A A371902 _Federico Provvedi_, Apr 13 2024