|
|
A214927
|
|
Number of n-digit numbers N that do not end with 0 and are such that the reversal of N divides N but is different from N.
|
|
31
|
|
|
0, 0, 0, 2, 2, 2, 2, 4, 4, 6, 6, 10, 10, 16, 16, 26, 26, 42, 42, 68, 68, 110, 110, 178, 178, 288, 288, 466, 466, 754, 754, 1220, 1220, 1974, 1974, 3194, 3194, 5168, 5168, 8362, 8362, 13530, 13530, 21892, 21892, 35422, 35422, 57314, 57314, 92736, 92736, 150050, 150050, 242786, 242786, 392836, 392836, 635622, 635622
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,4
|
|
COMMENTS
|
For the actual numbers, see A031877 and their reversals in A008919. See especially the comments in A008919.
|
|
REFERENCES
|
W. W. R. Ball and H. S. M. Coxeter. Mathematical Recreations and Essays, Macmillan, New York, 1939, page 13; Dover, New York, 13th ed. 1987, pp. 14-15.
H. Camous, Jouer Avec Les Maths, "Cardinaux Réversibles", Section I, Problem 6, pp. 27, 37-38; Les Editions D'Organisation, Paris, 1984.
Heinrich Dörrie, Mathematische Miniaturen, Ferdinand Hirt, Breslau, Germany, 1943; see pages 337-339.
M. Gardner, Mathematical Magic Show, Vintage Books, 1978, pp. 203, 204, 211, 212.
C. A. Grimm and D. W. Ballew, Reversible multiples, J. Rec. Math. 8 (1975-1976), 89-91.
D. Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, London, 1986, Entry 1089.
|
|
LINKS
|
J. Jonesco (proposer), E.-N. Barisien and [no initials given] Welsch (solvers), Problem 1622, L'Intermédiaire des mathématiciens, VI (1899), p. 200; L'Intermédiaire des mathématiciens, XV (1908), pp. 132-133, pp. 278-279 (in French).
|
|
FORMULA
|
a(n) = 2*Fibonacci(floor((n-2)/2)) = 2*A103609(n-2).
G.f.: -2*x^4*(x+1) / (x^4+x^2-1). - Colin Barker, Dec 31 2013
|
|
EXAMPLE
|
The smallest examples of such numbers are 8712 and 9801 (so a(n)=0 for n < 4, a(4) = 2); 87912 and 98901 (so a(5) = 2); and 879912 and 989901 (so a(6) = 2).
|
|
MATHEMATICA
|
Join[{0}, Table[2 Fibonacci[Floor[(n - 2) / 2]], {n, 2, 60}]] (* Vincenzo Librandi, Jun 18 2013 *)
|
|
PROG
|
(Magma) [0] cat [2*Fibonacci(Floor((n-2)/2)): n in [2..60]]; // Vincenzo Librandi, Jun 18 2013
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
Formula, more terms and additional references and links from N. J. A. Sloane, Mar 11 2013
|
|
STATUS
|
approved
|
|
|
|