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A016113
Numbers whose square is a palindrome with an even number of digits.
4
836, 798644, 64030648, 83163115486, 6360832925898, 69800670077028, 98275825201587, 6819209882215742, 40447213778058769, 404099764753665981, 633856150760638652, 795559265009384106, 637323988797048057098, 3823177109095314778621
OFFSET
1,1
COMMENTS
Further terms, listed on P. De Geest's page, are 722956456358957313434535, 831775153121251039203514, 4275548277509699161443659 and 64897400105515621177314682. - M. F. Hasler, Jun 08 2014
For the squares, see A027829(n) = a(n)^2. - M. F. Hasler, Oct 11 2019
REFERENCES
C. Ashbacher, More on palindromic squares, J. Rec. Math. 22, no. 2 (1990), 133-135. [A scan of the first page of this article is included with the last page of the Keith (1990) scan]
LINKS
P. De Geest, Palindromic Squares
M. Keith, Classification and enumeration of palindromic squares, J. Rec. Math., 22 (No. 2, 1990), 124-132. [Annotated scanned copy]
F. Yuan, Palindromic Square Numbers, as of July 2002.
PROG
(PARI) is_A016113(n)={Vecrev(n=digits(n^2))==n&&!bittest(#n, 0)} \\ This is faster than first checking for even length, if applied to numbers in a range where the squares are known to have an even number of digits, as should be the case for a systematic search. - M. F. Hasler, Jun 08 2014
CROSSREFS
Cf. A027829. A proper subset of A002778.
Sequence in context: A138850 A357326 A322524 * A177846 A167603 A284187
KEYWORD
nonn,base
EXTENSIONS
Two new terms were recently found by Bennett from UK (communication from Patrick De Geest)
Edited by M. F. Hasler, Jun 08 2014
Missing a(10) inserted by M. F. Hasler, Oct 11 2019
STATUS
approved