cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A016113 Numbers whose square is a palindrome with an even number of digits.

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%I A016113 #34 Apr 02 2025 18:04:01
%S A016113 836,798644,64030648,83163115486,6360832925898,69800670077028,
%T A016113 98275825201587,6819209882215742,40447213778058769,404099764753665981,
%U A016113 633856150760638652,795559265009384106,637323988797048057098,3823177109095314778621
%N A016113 Numbers whose square is a palindrome with an even number of digits.
%C A016113 For the squares, see A027829(n) = a(n)^2. - _M. F. Hasler_, Oct 11 2019
%D A016113 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]
%H A016113 Max Alekseyev, <a href="/A016113/b016113.txt">Table of n, a(n) for n = 1..22</a> (from Patrick De Geest's website)
%H A016113 K. S. Brown, <a href="http://www.mathpages.com/home/kmath359.htm">On General Palindromic Numbers</a>
%H A016113 Patrick De Geest, <a href="https://www.worldofnumbers.com/nobase10pg2.htm">Palindromic Squares in bases 2 to 17</a>
%H A016113 P. De Geest, <a href="https://www.worldofnumbers.com/subsquar.htm">Subsets of Palindromic Squares</a>
%H A016113 M. Keith, <a href="/A002778/a002778_1.pdf">Classification and enumeration of palindromic squares</a>, J. Rec. Math., 22 (No. 2, 1990), 124-132. [Annotated scanned copy]
%H A016113 F. Yuan, <a href="http://www.fengyuan.com/palindrome.html">Palindromic Square Numbers</a>, as of July 2002.
%o A016113 (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
%Y A016113 A proper subset of A002778.
%Y A016113 Cf. A027829.
%K A016113 nonn,base
%O A016113 1,1
%A A016113 _Robert G. Wilson v_
%E A016113 Two terms were found by Bennett from UK (communication from _Patrick De Geest_)
%E A016113 Edited by _M. F. Hasler_, Jun 08 2014
%E A016113 Missing a(10) inserted by _M. F. Hasler_, Oct 11 2019