OFFSET
1,1
COMMENTS
Subsequence of A206926.
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.
Example: a(19) = 615830 = 10010110010110_2 = concatenate('100101','100101','10').
LINKS
Hieronymus Fischer, Table of n, a(n) for n = 1..500
Index entries for linear recurrences with constant coefficients, signature (2,0,0,0,0,1,-2).
FORMULA
a(n) = 37*2^(1+n mod 6)*(2^(6*floor(n/6))-1)/63 + floor(37*2^(n mod 6)/2^5).
A206925(a(n)) = 2*floor(log_2(a(n))).
From Hieronymus Fischer, Jan 13 2013: (Start)
a(n) = floor((37*2^(n+1)/63)) mod 2^(n+1).
a(n+1) = 2*a(n) + floor(37*2^(n+2)/63) mod 2. (End)
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
G.f.: x*(2+x^2+x^4+x^5-2*x^6)/((1-2*x)*(1-x^6)).
EXAMPLE
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.
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.
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Hieronymus Fischer, Mar 24 2012
STATUS
approved