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 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
KEYWORD
base,nonn
AUTHOR
Dremov Dmitry (dremovd(AT)gmail.com), May 01 2009
STATUS
approved