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A162751
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Write down in binary the n-th 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.
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3
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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
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1,3
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COMMENTS
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Every positive integer occurs exactly twice in this sequence.
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LINKS
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FORMULA
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a(1) = a(2) = 1; for i >= 2, a(2 i-1) = 2 a(i-1) and a(2 i) = 2 a(i-1) + 1. Robert Israel, Apr 03 2014
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EXAMPLE
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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.
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MAPLE
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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^(i-1), 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((n-1)/2)
else 2*procname(n/2-1)+1
end if
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MATHEMATICA
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a[n_] := a[n] = If[n <= 2, 1, If[OddQ[n], 2 a[(n-1)/2], 2 a[n/2-1] + 1]];
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PROG
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(PARI) a(n) = n++; my(L = logint(n, 2)); n - 1 << (L - !bittest(n, L-1)) \\ Mikhail Kurkov, Mar 13 2024
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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