A066531 Numbers which can be expressed as the product of a number and its reversal in at least two different ways.

2520, 4030, 5740, 7360, 7650, 9760, 10080, 12070, 13000, 14580, 14620, 16120, 17290, 18550, 19440, 22680, 22960, 24300, 25200, 26680, 27010, 29440, 31540, 34780, 36270, 36400, 40300, 40320, 42750, 46060, 49300, 50920, 56050, 57400

Offset: 1

Author

Robert G. Wilson v, Jan 06 2002

Keywords

• base
• nonn

Comments

The digital root of these terms is always 1,4,7 or 9.

Examples

			4030 = 130 * 031 = 310 * 013, 144648 = 861 * 168 = 492 * 294, 185472 = 672 * 276 = 384 * 483, 9949716 = 2583 * 3852 = 1476 * 6741, 16746912 = 2556 * 6552 = 4473 * 3744, etc.
		

References

• S. S. Gupta, EPRNs, Science Today, Feb. 1987, India.

Links

• Hans Havermann, Table of n, a(n) for n = 1..10000
• Shyam Sunder Gupta, EPRN Numbers
• Shyam Sunder Gupta, Equal Product of Reversible Numbers (EPRN), Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 12, 353-365.

Programs

Mathematica

f[n_] := (r = FromDigits[Reverse[IntegerDigits[n]]]; If[n >= r, n*r, 0]);s = Sort[DeleteCases[Table[f[i], {i, 10^4}], 0]]; Union[s[[Select[Range[Length[s]] - 1, s[[#]] == s[[# + 1]] &]]]]
Take[Select[Tally[Table[If[n1&][[All,1]]//Union,40] (* Harvey P. Dale, Aug 28 2021 *)

Extensions

Edited by Hans Havermann, Feb 11 2012

Definition rewritten by N. J. A. Sloane, Aug 01 2019