A206642 -id:A206642 - cp's OEIS frontend

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

Shyam Sunder Gupta, Jun 07 2003

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

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

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

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.

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).

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

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

A117281 Palindromes whose squares belong to A066531.

Original entry on oeis.org

252, 2772, 20502, 23632, 25452, 26962, 27972, 48384, 225522, 252252, 259952, 279972, 619916, 1113111, 1226221, 1357531, 2005002, 2070702, 2126212, 2150512, 2216122, 2226222, 2249422, 2275722, 2316132, 2347432, 2386832, 2429242

Offset: 1

Lekraj Beedassy, Apr 23 2006

a(n)^2 = A083408(k) for some k.

			27972 is in the sequence because 782432784 = 27972*27972 = 15984*48951.
1113111 is in the sequence because 1239016098321 = 1113111*1113111 = 1022121*1212201.

Chai Wah Wu, Table of n, a(n) for n = 1..4679 (n = 1..54 from Hans Havermann)
Shyam Sunder Gupta, EPRNs

Cf. A066531, A083408 (square EPRNs), A206642.

Edited and corrected by Klaus Brockhaus, Aug 21 2007

Edited by N. J. A. Sloane, Aug 01 2019

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

Programs

PARI

Extensions