

A162751


Write down in binary the nth positive (odd) integer that is a palindrome in base 2. Take only the leftmost half of the digits (including the middle digit if there are an odd number of digits). a(n) is the decimal equivalent of the result.


3



1, 1, 2, 3, 2, 3, 4, 5, 6, 7, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44
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OFFSET

1,3


COMMENTS

Every positive integer occurs exactly twice in this sequence.


LINKS



FORMULA

a(1) = a(2) = 1; for i >= 2, a(2 i1) = 2 a(i1) and a(2 i) = 2 a(i1) + 1. Robert Israel, Apr 03 2014


EXAMPLE

27 is the 9th (odd) palindrome when written in binary. 27 in binary is 11011. Take the leftmost half of the digits (including the middle digit), and we have 110. a(9) is decimal equivalent of this, which is 6.


MAPLE

read("transforms3") ; a006995 := BFILETOLIST("b006995.txt") ; chop := proc(L) [op(1.. floor((nops(L)+1)/2), L)] ; end: for n from 2 to 100 do p := op(n, a006995) ; bdgs := chop(convert(p, base, 2)) ; add(op(i, bdgs)*2^(i1), i=1..nops(bdgs)) ; printf("%d, ", %) ; end do: # R. J. Mathar, Aug 01 2009
if n <= 2 then 1
elif n::odd then 2*procname((n1)/2)
else 2*procname(n/21)+1
end if


MATHEMATICA

a[n_] := a[n] = If[n <= 2, 1, If[OddQ[n], 2 a[(n1)/2], 2 a[n/21] + 1]];


CROSSREFS



KEYWORD

base,nonn


AUTHOR



EXTENSIONS



STATUS

approved



