A285986 Numbers that are never cyclops for any base b > 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

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

Cf. A134808.

Sequence in context: A330120 A239015 A030706 * A101883 A236207 A225837

Adjacent sequences: A285983 A285984 A285985 * A285987 A285988 A285989

Keyword

nonn,base

Author

Rémy Sigrist, Apr 30 2017

Status

approved