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A285986
Numbers that are never cyclops for any base b > 1.
1
1, 2, 3, 4, 6, 7, 8, 9, 12, 13, 14, 15, 16, 21, 22, 23, 24, 25, 30, 31, 32, 36, 42, 43, 44, 45, 46, 47, 48, 56, 57, 58, 59, 60, 61, 62, 63, 64, 72, 80, 81, 90, 91, 92, 93, 94, 95, 96, 97, 98, 114, 117, 118, 120, 121, 136, 137, 138, 141, 144, 156, 157, 158, 159
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
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
Cf. A134808.
Sequence in context: A330120 A239015 A030706 * A101883 A236207 A375018
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Apr 30 2017
STATUS
approved