

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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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), 133135. [A scan of the first page of this article is included with the last page of the Keith (1990) scan]


LINKS

Table of n, a(n) for n=1..14.
K. S. Brown, On General Palindromic Numbers
P. De Geest, Palindromic Squares
P. De Geest, Subsets of Palindromic Squares
M. Keith, Classification and enumeration of palindromic squares, J. Rec. Math., 22 (No. 2, 1990), 124132. [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: A162945 A138850 A322524 * A177846 A167603 A284187
Adjacent sequences: A016110 A016111 A016112 * A016114 A016115 A016116


KEYWORD

nonn,base


AUTHOR

Robert G. Wilson v


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



