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A325150
Squares which can be expressed as the product of a number and its reversal in exactly two ways.
8
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.
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).
Sequence in context: A076750 A083406 A083408 * A072693 A119276 A145437
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