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 A160078 Positive integers which apparently never result in a palindrome under repeated applications of the function f(x) = x + (x with digits in binary expansion reversed). Binary analog of Lychrel numbers. 0
 22, 26, 28, 35, 37, 41, 45, 46, 47, 49, 60, 61, 67, 75, 77, 78, 84, 86, 89, 90, 93, 94, 95, 97, 105, 106, 108, 110, 116, 120, 122, 124, 125, 131, 135, 139, 141, 147, 149, 152 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Number of iterations equals 1000, but all non-seeded numbers (under) fall out in 32 iterations LINKS Diofant.ru Problem: binary Lychrel numbers under 1024. (Russian language!) [From Dremov Dmitry (dremovd(AT)gmail.com), May 03 2009] EXAMPLE 22 = 10110 10110 + 01101 = 100011 100011 + 110001 = 1010100... Not forming polyndrom in 1000 iterations. PROG (Python) def toSystem( n, k ) : ....d = [] ....while n > 0 : ........d.append( n % k ) ........n /= k ....return d[ -1::-1] def makeint( l, system = 10 ) : ....i = 0 ....for d in l : ........i = i * system + d ....return i maxn = 1024 it = [] for i in range( 1, maxn ) : ....d = toSystem( i, 2 ) ....isLychrel = True ....for j in range( 1000 ) : ........d = toSystem( makeint( d, 2 ) + makeint( d[::-1], 2 ), 2 ) ........if d == d[::-1] : ............it.append( j + 1 ) ............isLychrel = False ............break ....if isLychrel : ........it.append( 0 ) print 'Maximum iterations for non-seed numbers', max( it ) Lychrel = [] for i in range( len(it) ) : ....if it[i] == 0 : ........Lychrel.append( i + 1 ) print 'Count of binary Lychrel numbers', len( Lychrel ) print 'All binary lichler under', maxn print 'Decimal form', Lychrel print 'Binary form', map( lambda x: ''.join( map( str, toSystem( x, 2 ) ) ), Lychrel ) CROSSREFS Binary A023108 Sequence in context: A124177 A260990 A260991 * A066059 A084891 A162422 Adjacent sequences:  A160075 A160076 A160077 * A160079 A160080 A160081 KEYWORD base,nonn AUTHOR Dremov Dmitry (dremovd(AT)gmail.com), May 01 2009 STATUS approved

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Last modified May 31 22:45 EDT 2020. Contains 334756 sequences. (Running on oeis4.)