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.

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

Offset

1,1

Comments

Number of iterations equals 1000, but all non-seeded numbers (under) fall out in 32 iterations

Links

Table of n, a(n) for n=1..40.

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 a palindrome after 1000 iterations.

Prog

(Python)
from sympy.ntheory.digits import digits
def make_int(l, b):
    return int(''.join(str(d) for d in l), b)
maxn = 102
it = []
for i in range( 1, maxn ) :
    d = digits( i, 2 )[1:]
    isLychrel = True
    for j in range( 1000 ) :
        d = digits( make_int( d, 2 ) + make_int( d[::-1], 2 ), 2 )[1:]
        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', list(map( lambda x: ''.join( map( str, toSystem( x, 2 ) ) ), Lychrel )))

Crossrefs

Binary version of 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