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

1,1

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.

Links

Table of n, a(n) for n=1..13.

Shou'en Wang, Binary reversal (Chinese)

Example

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.

Crossrefs

Cf. A066531, A066598.

Sequence in context: A058445 A290540 A132910 * A172550 A216908 A080126

Adjacent sequences: A386218 A386219 A386220 * A386222 A386223 A386224

Keyword

nonn,base

Author

Zhao Hui Du, Aug 12 2025

Status

approved