A325150 Squares which can be expressed as the product of a number and its reversal in exactly two ways.

63504, 435600, 7683984, 16240900, 25401600, 66585600, 420332004, 558471424, 647804304, 726949444, 782432784, 1067328900, 1624090000, 1897473600, 2341011456, 2540160000, 6658560000, 50860172484, 52587662400, 63631071504, 67575042304, 78384320784, 96118600900, 106732890000

Offset: 1

Author

Bernard Schott, Apr 03 2019

Keywords

• nonn
• base

Comments

When q = m^2 does not end with a 0 is a term, then m is a palindrome belonging to A117281.

When q = m^2 ending with a 0 is a term, then either m = r * 10^u where r belongs to A325151 and u >= 1, or m is in A342994.

Examples

			1) Squares without trailing zeros:
Even square: 7683984 = 2772^2 = 2772 * 2772 = 1584 * 4851.
Odd square: 1239016098321 = 1113111^2 = 1113111 * 1113111 = 1022121 * 1212201.
2) Squares with trailing zeros:
1st case: 16240900 = 4030^2 = 16900 * 961 = 96100 * 169.
2nd case: 435600 = 660^2 = 6600 * 66 = 528 * 825.
		

References

• D. Wells, 63504 entry, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1997, p. 168.

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..1672
• David A. Corneth, Examples of factorizations of terms in exactly two or three ways.
• Shyam Sunder Gupta, EPRN Numbers.

Crossrefs

Cf. A325148 (at least one way), A325149 (only one way), A083408 (at least two ways), A307019 (exactly three ways).

Cf. A083407 (odd squares), A083408 (even squares without trailing 0's).

Cf. A117281, A325151, A342994.

Extensions

Corrected terms by Chai Wah Wu, Apr 12 2019

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