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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 (list; graph; refs; listen; history; text; internal format)
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: A320456 A239015 A030706 * A101883 A236207 A225837

Adjacent sequences:  A285983 A285984 A285985 * A285987 A285988 A285989

KEYWORD

nonn,base

AUTHOR

Rémy Sigrist, Apr 30 2017

STATUS

approved

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Last modified August 24 23:01 EDT 2019. Contains 326314 sequences. (Running on oeis4.)