Demlo Number

The initially Palindromic Numbers 1, 121, 12321, 1234321, 123454321, ... (Sloane's A002477). For the first through ninth terms, the sequence is given by the Generating Function

$$-{10x+1\over(x-1)(10x-1)(100x-1)}=1+121x+12321x^2+1234321x^3+\ldots$$

(Plouffe 1992, Sloane and Plouffe 1995). The definition of this sequence is slightly ambiguous from the tenth term on.

See also Consecutive Number Sequences, Palindromic Number

References

Kaprekar, D. R. ``On Wonderful Demlo Numbers.'' Math. Student 6, 68-70, 1938.

Plouffe, S. ``Approximations de Séries Génératrices et quelques conjectures.'' Montréal, Canada: Université du Québec à Montréal, Mémoire de Maîtrise, UQAM, 1992.

Sloane, N. J. A. Sequence A002477/M5386 in ``An On-Line Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.