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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 (list; graph; refs; listen; history; text; internal format)
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 all-1'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 (n-1)/2 bits and the reverse of the right (n-1)/2 bits is the all-1'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..(d-1)/2]), 1, op(L[(d+1)/2..-1])], M[d-1]);

  if d < N then

    M[d+1]:= map(L -> ([op(L[1..(d-1)/2]), 0, 1, op(L[(d+1)/2..-1])], [op(L[1..(d-1)/2]), 1, 0, op(L[(d+1)/2..-1])]), M[d-1])

  fi

od:

seq(seq(add(L[-i]*2^(i-1), 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[#b-k+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

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Last modified June 18 07:04 EDT 2019. Contains 324203 sequences. (Running on oeis4.)