Palindromic Number

A symmetrical number which is written in some base $b$ as $a_1\,a_2\,\dots\,a_2\,a_1$. The first few are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 111, 121, ... (Sloane's A002113).

The first few $n$ for which the Pronic Number $P_n$ is palindromic are 1, 2, 16, 77, 538, 1621, ... (Sloane's A028336), and the first few palindromic numbers which are Pronic are 2, 6, 272, 6006, 289982, ... (Sloane's A028337). The first few numbers whose squares are palindromic are 1, 2, 3, 11, 22, 26, ... (Sloane's A002778), and the first few palindromic squares are 1, 4, 9, 121, 484, 676, ... (Sloane's A002779).

See also Demlo Number, Palindromic Number Conjecture, Reversal

References

De Geest, P. ``Palindromic Products of Two Consecutive Integers.'' http://www.ping.be/~ping6758/consec.htm.

De Geest, P. ``Palindromic Squares.'' http://www.ping.be/~ping6758/square.htm.

Pappas, T. ``Numerical Palindromes.'' The Joy of Mathematics. San Carlos, CA: Wide World Publ./Tetra, p. 146, 1989.

Sloane, N. J. A. A028336, A028337 A002113/M0484, A002778/M0907, and A002779/M3371 in ``An On-Line Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html.