A386221 Numbers which can be expressed as the product of a number and its binary reversal in at least three different ways.

2371610879733375, 8379443074856875, 103889625367330285, 162508095102648823, 2143169709271976875, 2481725627762299375, 4055619414785589625, 8167773178498814075, 9027536760163222895, 133527604616779133915, 133893081609954481115, 137216105281788994475, 457495296809227508125

Offset: 1

Author

Zhao Hui Du, Aug 12 2025

Keywords

• nonn
• base
• new

Comments

It appears that most numbers that can be expressed in three different ways can also be expressed in four different ways. For a(n) < 2^88, only 11 numbers can be expressed in exactly three ways while 691 numbers can be expressed in exactly four ways.

Examples

			2371610879733375 = 51606261*45955875 = 64244529*36915375 = 64338225*36861615 while 51606261 = 11000100110111001011110101_2, 45955875 = 10101111010011101100100011_2 and reverse(11000100110111001011110101) = 10101111010011101100100011.
8379443074856875 = 101377465*82655875 = 102886105*81443875 = 114021425*73490075 = 115718225*72412475.
		

Links

• Shou'en Wang, Binary reversal (Chinese)

Crossrefs

Cf. A066531, A066598.