|
| |
|
|
A134808
|
|
Cyclops numbers.
|
|
20
| |
|
|
0, 101, 102, 103, 104, 105, 106, 107, 108, 109, 201, 202, 203, 204, 205, 206, 207, 208, 209, 301, 302, 303, 304, 305, 306, 307, 308, 309, 401, 402, 403, 404, 405, 406, 407, 408, 409, 501, 502, 503, 504, 505, 506, 507, 508, 509, 601, 602, 603, 604, 605, 606
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| Numbers with middle digit 0, that have only one digit 0, and the total number of digits is odd; the digit 0 represents the eye of a cyclops.
|
|
|
EXAMPLE
| 109 is a cyclops number because 109 has only one digit 0 and this 0 is the middle digit.
|
|
|
MATHEMATICA
| cyclopsQ[n_Integer, b_:10] := Module[{digitList = IntegerDigits[n, b], len, pos0s, flag}, len = Length[digitList]; pos0s = Select[Range[len], digitList[[#]] == 0 &]; flag = OddQ[len] && (Length[pos0s] == 1) && (pos0s == {(len + 1)/2}); Return[flag]]; Select[Range[0, 999], cyclopsQ] (* From Alonso del Arte, alonso.delarte(AT)gmail.com, Dec 16 2010 *)
Reap[Do[id=IntegerDigits[n]; If[Position[id, 0]=={{(Length[id]+1)/2}}, Sow[n]], {n, 0, 10^3}]][[2, 1]] (* Zak Seidov *)
|
|
|
PROG
| (Sage)
def is_cyclops(n, base=10):
....dg = n.digits(base) if n > 0 else [0]
....return len(dg) % 2 == 1 and dg[len(dg)//2] == 0 and dg.count(0) == 1
is_A134808 = lambda n: is_cyclops(n) # [D. S. McNeil, Dec 17 2010]
|
|
|
CROSSREFS
| Cf. A134809, A138131, A138148, A160717, A182809.
Sequence in context: A043639 A152054 A183086 * A164849 A162671 A030474
Adjacent sequences: A134805 A134806 A134807 * A134809 A134810 A134811
|
|
|
KEYWORD
| base,easy,nonn
|
|
|
AUTHOR
| Omar E. Pol (info(AT)polprimos.com), Nov 21 2007
|
| |
|
|
