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

1,1

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.

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.

Example

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.

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.

Sequence in context: A076750 A083406 A083408 * A072693 A119276 A145437

Adjacent sequences: A325147 A325148 A325149 * A325151 A325152 A325153

Keyword

nonn,base

Author

Bernard Schott, Apr 03 2019

Extensions

Corrected terms by Chai Wah Wu, Apr 12 2019

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

Status

approved