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

836, 798644, 64030648, 83163115486, 6360832925898, 69800670077028, 98275825201587, 6819209882215742, 40447213778058769, 404099764753665981, 633856150760638652, 795559265009384106, 637323988797048057098, 3823177109095314778621

Offset: 1

Author

Robert G. Wilson v

Keywords

• nonn
• base

Comments

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

• Max Alekseyev, Table of n, a(n) for n = 1..22 (from Patrick De Geest's website)
• K. S. Brown, On General Palindromic Numbers
• Patrick De Geest, Palindromic Squares in bases 2 to 17
• P. De Geest, Subsets of 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.

Crossrefs

A proper subset of A002778.

Cf. A027829.

Programs

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

Extensions

Two terms were 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