

A249605


Dissectible numbers in the sense of Gunjikar and Kaprekar.


3



9, 18, 27, 36, 45, 54, 63, 72, 81, 108, 117, 126, 135, 144, 153, 162, 207, 216, 225, 234, 243, 306, 315, 324, 405
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

The numbers really have exactly three digits, allowing leading zeros. The full list is: 009, 018, 027, 036, 045, 054, 063, 072, 081, 108, 117, 126, 135, 144, 153, 162, 207, 216, 225, 234, 243, 306, 315, 324, 405.
A dissectible number is a threedigit number abc with the property that when multiplied by any Wonderful Demlo number (A002477) the product has the form axx..xbyy..yc, with the same number of x digits as y digits.


LINKS

K. R. Gunjikar and D. R. Kaprekar, Theory of Demlo numbers, J. Univ. Bombay, Vol. VIII, Part 3, Nov. 1939, pp. 39. [Annotated scanned copy]


EXAMPLE

9*12321 = 009*12321 = 0110889 (a=b=0, c=9, x=1, y=8).
162*121 = 19602 (here x=9, y=0).
162*12321 = 1996002 (again x=9, y=0).


CROSSREFS



KEYWORD

nonn,fini,full,base


AUTHOR



STATUS

approved



