

A277238


Folding numbers (see comments for the definition).


4



1, 2, 6, 10, 12, 22, 28, 38, 42, 52, 56, 78, 90, 108, 120, 142, 150, 170, 178, 204, 212, 232, 240, 286, 310, 346, 370, 412, 436, 472, 496, 542, 558, 598, 614, 666, 682, 722, 738, 796, 812, 852, 868, 920, 936, 976, 992, 1086, 1134, 1206, 1254, 1338, 1386, 1458, 1506, 1596, 1644, 1716, 1764, 1848, 1896, 1968
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OFFSET

1,2


COMMENTS

Folding numbers: Numbers with an even number of bits in their binary expansion such that the XOR of the left half and the reverse of the right half is the all1's string. Numbers with an odd number of bits in their binary expansion such that the central bit is 1, and the XOR of the left (n1)/2 bits and the reverse of the right (n1)/2 bits is the all1's string.
Folding numbers with an even (resp. odd) number of bits form A035928 (resp. A276795).  N. J. A. Sloane, Nov 03 2016


LINKS

Lars Blomberg, Table of n, a(n) for n = 1..10000
Stack Exchange, Programming Puzzles and Code Golf: Folding Numbers


EXAMPLE

178 in base 2 is 10110010. Taking the XOR of 1011 and 0100 (which is 0010 reversed) gives the result 1111, so 178 is in the sequence.


MAPLE

N:= 16: # to get all terms < 2^N
M[1]:= [[1]]: M[2]:= [[1, 0]]:
for d from 3 to N by 2 do
M[d]:= map(L > [op(L[1..(d1)/2]), 1, op(L[(d+1)/2..1])], M[d1]);
if d < N then
M[d+1]:= map(L > ([op(L[1..(d1)/2]), 0, 1, op(L[(d+1)/2..1])], [op(L[1..(d1)/2]), 1, 0, op(L[(d+1)/2..1])]), M[d1])
fi
od:
seq(seq(add(L[i]*2^(i1), i=1..d), L=M[d]), d=1..N); # Robert Israel, Nov 09 2016


MATHEMATICA

{1}~Join~Select[Range@ 2000, If[OddQ@ Length@ # && Take[#, {Ceiling[ Length[#]/2]}] == {0}, False, Union[Take[#, Floor[Length[#]/2]] + Reverse@ Take[#, Floor[Length[#]/2]]] == {1}] &@ IntegerDigits[#, 2] &] (* Michael De Vlieger, Oct 07 2016 *)


PROG

(PARI) isok(n) = {if (n==1, return(1)); b = binary(n); if ((#b % 2) && (b[#b\2+1] == 0), return (0)); vecmin(vector(#b1, k, bitxor(b[k], b[#bk+1]))) == 1; } \\ Michel Marcus, Oct 07 2016


CROSSREFS

Cf. A035928, A276795.
Sequence in context: A028348 A214963 A140776 * A108783 A235989 A066679
Adjacent sequences: A277235 A277236 A277237 * A277239 A277240 A277241


KEYWORD

nonn,base


AUTHOR

Taylor J. Smith, Oct 06 2016


STATUS

approved



