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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: 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

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Last modified April 19 21:57 EDT 2021. Contains 343117 sequences. (Running on oeis4.)