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%I #29 Apr 24 2024 09:38:39
%S 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,
%T 15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,16,17,18,19,20,21,
%U 22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44
%N 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.
%C Every positive integer occurs exactly twice in this sequence.
%H Robert Israel, <a href="/A162751/b162751.txt">Table of n, a(n) for n = 1..10000</a>
%F 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
%e 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.
%p 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
%p A162751:= proc(n) option remember;
%p if n <= 2 then 1
%p elif n::odd then 2*procname((n-1)/2)
%p else 2*procname(n/2-1)+1
%p end if
%p end proc; # _Robert Israel_, Apr 03 2014
%t a[n_] := a[n] = If[n <= 2, 1, If[OddQ[n], 2 a[(n-1)/2], 2 a[n/2-1] + 1]];
%t Array[a, 75] (* _Jean-François Alcover_, Apr 06 2020, after _Robert Israel_ *)
%Y Cf. A006995.
%K base,nonn,changed
%O 1,3
%A _Leroy Quet_, Jul 12 2009
%E More terms from _R. J. Mathar_, Aug 01 2009
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