OFFSET
1,2
COMMENTS
A134808 gives the definition of cyclops numbers for base 10; we can naturally generalize this notion for any base b > 1.
LINKS
Rémy Sigrist, Table of n, a(n) for n = 1..10000
EXAMPLE
The following table indicates why 42 is not cyclops for any base b > 1:
b 42 in base b Reason
- ------------ ------
2 1,0,1,0,1,0 Even number of digits
3 1,1,2,0 Even number of digits
4 2,2,2 No middle 0
5 1,3,2 No middle 0
6 1,1,0 No middle 0
7 6,0 Even number of digits
... X,X Even number of digits
42 1,0 Even number of digits
>42 42 No middle 0
Hence 42 appears in the sequence.
The number 51 is cyclops for bases 4 (303), 5 (201) and 7 (102); hence 51 does not appear in the sequence.
PROG
(PARI) is(n) = if (n==0, return (0)); my (base=2); while (1, my (d=digits(n, base)); if (#d<3, return (1)); if (#d%2==1 && d[(#d+1)/2]==0 && sum(i=1, #d, 1-sign(d[i]))==1, return (0)); base++)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Apr 30 2017
STATUS
approved