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A285986 Numbers that are never cyclops for any base b > 1. 1

%I

%S 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,

%T 45,46,47,48,56,57,58,59,60,61,62,63,64,72,80,81,90,91,92,93,94,95,96,

%U 97,98,114,117,118,120,121,136,137,138,141,144,156,157,158,159

%N Numbers that are never cyclops for any base b > 1.

%C A134808 gives the definition of cyclops numbers for base 10; we can naturally generalize this notion for any base b > 1.

%H Rémy Sigrist, <a href="/A285986/b285986.txt">Table of n, a(n) for n = 1..10000</a>

%e The following table indicates why 42 is not cyclops for any base b > 1:

%e b 42 in base b Reason

%e - ------------ ------

%e 2 1,0,1,0,1,0 Even number of digits

%e 3 1,1,2,0 Even number of digits

%e 4 2,2,2 No middle 0

%e 5 1,3,2 No middle 0

%e 6 1,1,0 No middle 0

%e 7 6,0 Even number of digits

%e ... X,X Even number of digits

%e 42 1,0 Even number of digits

%e >42 42 No middle 0

%e Hence 42 appears in the sequence.

%e The number 51 is cyclops for bases 4 (303), 5 (201) and 7 (102); hence 51 does not appear in the sequence.

%o (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++)

%Y Cf. A134808.

%K nonn,base

%O 1,2

%A _Rémy Sigrist_, Apr 30 2017

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Last modified May 10 04:03 EDT 2021. Contains 343748 sequences. (Running on oeis4.)