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A285767
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Cyclops octagonal numbers: a(n) = n*(3*n-2) with one "zero" digit in the middle.
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0
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0, 408, 11041, 18096, 22016, 23056, 28033, 38081, 56033, 61061, 1140833, 1170625, 1250656, 1410416, 1460216, 1540833, 2120161, 2130261, 2140385, 2150533, 2310896, 2390561, 2460696, 2520833, 2570576, 2780181, 2920533, 3230256, 3280256, 3490565, 3660865, 3680776
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OFFSET
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1,2
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COMMENTS
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The n-th octagonal number x(n) = n*(3*n - 2).
All the terms have the number of digits odd with only one "zero" digit in the middle.
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LINKS
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EXAMPLE
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For n = 12; x(12) = 12*(3*12 - 2) = 408 that is 12th octagonal number with one zero digit in the middle, hence appears in the sequence.
For n = 61; x(61) = 61*(3*61 - 2) = 11041 that is 61st octagonal number with one zero digit in the middle, hence appears in the sequence.
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MAPLE
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iscyclops:= proc(n) local L, t;
t:= ilog10(n);
if t::odd then return false fi;
L:= convert(n, base, 10);
L[1+t/2] = 0 and numboccur(0, L) = 1
end proc:
iscyclops(0):= true:
select(iscyclops, [seq(n*(3*n-2), n=0..1000)]);
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MATHEMATICA
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Select[Table[n (3 n - 2), {n, 0, 1110}], And[OddQ@ Length@ #, Count[#, 0] == 1, Take[#, {Ceiling[Length[#]/2]}] == {0}] &@ IntegerDigits@ # &] (* Michael De Vlieger, Apr 26 2017 *)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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