

A206927


Minimal numbers of binary length n+1 such that the number of contiguous palindromic bit patterns in the binary representation is minimal.


4



2, 4, 9, 18, 37, 75, 150, 300, 601, 1202, 2405, 4811, 9622, 19244, 38489, 76978, 153957, 307915, 615830, 1231660, 2463321, 4926642, 9853285, 19706571, 39413142, 78826284, 157652569, 315305138, 630610277, 1261220555
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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).
a(n) = floor((37*2^(n+1)/63)) mod 2^(n+1).
A206925(a(n)) = 2*floor(log_2(a(n))).
a(n+1) = 2a(n) + floor(37*2^(n+2)/63) mod 2.
G.f. x*( 2+x^2+x^4+x^52*x^6 ) / ( (x1)*(2*x1)*(1+x)*(x^2x+1)*(1+x+x^2) ).  R. J. Mathar, Apr 02 2012
Also, g.f. x*(2+x^2+x^4+x^52*x^6)/((12*x)*(1x^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

Cf. A006995, A206923  A206926, A070939.
Sequence in context: A182028 A081253 A118255 * A019299 A052932 A018097
Adjacent sequences: A206924 A206925 A206926 * A206928 A206929 A206930


KEYWORD

nonn,base


AUTHOR

Hieronymus Fischer, Mar 24 2012


EXTENSIONS

Further formulas added by Hieronymus Fischer, Jan 13 2013


STATUS

approved



