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 A162751 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. 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Every positive integer occurs exactly twice in this sequence. LINKS Robert Israel, Table of n, a(n) for n = 1..10000 FORMULA 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 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^(i-1), i=1..nops(bdgs)) ; printf("%d, ", %) ; end do: # R. J. Mathar, Aug 01 2009 A162751:= proc(n) option remember; if n <= 2 then 1 elif n::odd then 2*procname((n-1)/2) else 2*procname(n/2-1)+1 end if end proc; # Robert Israel, Apr 03 2014 MATHEMATICA a[n_] := a[n] = If[n <= 2, 1, If[OddQ[n], 2 a[(n-1)/2], 2 a[n/2-1] + 1]]; Array[a, 75] (* Jean-François Alcover, Apr 06 2020, after Robert Israel *) CROSSREFS Cf. A006995. Sequence in context: A358503 A327666 A286717 * A026342 A275727 A255395 Adjacent sequences: A162748 A162749 A162750 * A162752 A162753 A162754 KEYWORD base,nonn AUTHOR Leroy Quet, Jul 12 2009 EXTENSIONS More terms from R. J. Mathar, Aug 01 2009 STATUS approved

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Last modified August 5 22:15 EDT 2024. Contains 374957 sequences. (Running on oeis4.)