This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A206927 #27 Mar 19 2024 08:31:23
%S A206927 2,4,9,18,37,75,150,300,601,1202,2405,4811,9622,19244,38489,76978,
%T A206927 153957,307915,615830,1231660,2463321,4926642,9853285,19706571,
%U A206927 39413142,78826284,157652569,315305138,630610277,1261220555
%N A206927 Minimal numbers of binary length n+1 such that the number of contiguous palindromic bit patterns in the binary representation is minimal.
%C A206927 Subsequence of A206926.
%C A206927 From left to right, the binary representation of a(n) consists of a concatenation of the bit pattern 100101 (=37). If the number of places is not a multiple of 6, the least significant places are truncated. This leads to a simple linear recurrence.
%C A206927 Example: a(19)=615830=10010110010110_2=concatenate('100101','100101','10')
%H A206927 Hieronymus Fischer, <a href="/A206927/b206927.txt">Table of n, a(n) for n = 1..500</a>
%H A206927 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,0,0,0,1,-2).
%F A206927 a(n) = 37*2^(1+n mod 6)*(2^(6*floor(n/6))-1)/63 + floor(37*2^(n mod 6)/2^5).
%F A206927 a(n) = floor((37*2^(n+1)/63)) mod 2^(n+1).
%F A206927 A206925(a(n)) = 2*floor(log_2(a(n))).
%F A206927 a(n+1) = 2a(n) + floor(37*2^(n+2)/63) mod 2.
%F A206927 G.f.: x*( 2+x^2+x^4+x^5-2*x^6 ) / ( (x-1)*(2*x-1)*(1+x)*(x^2-x+1)*(1+x+x^2) ). - R. J. Mathar, Apr 02 2012
%F A206927 Also, g.f. x*(2+x^2+x^4+x^5-2*x^6)/((1-2*x)*(1-x^6)).
%e A206927 a(3)=9=1001_2 has 6 [=A206925(9)] contiguous palindromic bit patterns. This is the minimum value for binary numbers with 4 places and 9 is the least number with this property.
%e A206927 a(9)=601=1001011001_2 has 18 [=A206925(601)] contiguous palindromic bit patterns. This is the minimum value for binary numbers with 10 places and 601 is the least number with this property.
%Y A206927 Cf. A006995, A206923, A206924, A206925, A206926, A070939.
%K A206927 nonn,base
%O A206927 1,1
%A A206927 _Hieronymus Fischer_, Mar 24 2012
%E A206927 Further formulas added by _Hieronymus Fischer_, Jan 13 2013