A083408 Squares which can be expressed as the product of a number and its reversal in at least two different ways.

63504, 435600, 6350400, 7683984, 16240900, 25401600, 43560000, 66585600, 420332004, 558471424, 635040000, 647804304, 726949444, 768398400, 782432784, 1067328900, 1624090000, 1897473600, 2341011456, 2540160000, 4356000000, 6658560000, 42033200400, 50860172484, 52587662400

Offset: 1

Author

Shyam Sunder Gupta, Jun 07 2003

Keywords

• nonn
• base

Comments

Union of A083406 and A083407. - Lekraj Beedassy, Apr 23 2006

Examples

			63504 = 252 * 252 = 144 * 441,
1239016098321 = 1113111 * 1113111 = 1022121 * 1212201, etc.
635040000 = 144 * 4410000 = 252 * 2520000 = 441 * 1440000. - _David A. Corneth_, Mar 22 2019
		

References

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

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..2498 (n = 1..76 from Hans Havermann, n = 77..241 from David A. Corneth)
• David A. Corneth, Examples of factorizations of terms as described in Name.
• 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.

Crossrefs

Cf. A062917, A066531, A083406 (even), A083407 (odd), A070760, A117281 (palindromic square roots), A206642 (non-palindromic square roots), A325150 (products in exactly two different ways), A307019 (products in exactly three different ways).

Programs

PARI

is(n) = {if(!issquare(n), return(0)); my(d = divisors(n), t = 0); forstep(i = #d, #d \ 2 + 1, -1, revd = fromdigits(Vecrev(digits(d[i]))); if(revd * d[i] == n, t++; if(t >= 2, return(1)); ) ); 0 } \\ David A. Corneth, Mar 21 2019

Extensions

Corrected and extended by Hans Havermann, Feb 11 2012

a(21)-a(25) from David A. Corneth, Mar 21 2019

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