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%I #14 Aug 01 2023 15:37:13
%S 0,408,11041,18096,22016,23056,28033,38081,56033,61061,1140833,
%T 1170625,1250656,1410416,1460216,1540833,2120161,2130261,2140385,
%U 2150533,2310896,2390561,2460696,2520833,2570576,2780181,2920533,3230256,3280256,3490565,3660865,3680776
%N Cyclops octagonal numbers: a(n) = n*(3*n-2) with one "zero" digit in the middle.
%C The n-th octagonal number x(n) = n*(3*n - 2).
%C Subset of A000567.
%C All the terms have the number of digits odd with only one "zero" digit in the middle.
%e 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.
%e 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.
%p iscyclops:= proc(n) local L,t;
%p t:= ilog10(n);
%p if t::odd then return false fi;
%p L:= convert(n,base,10);
%p L[1+t/2] = 0 and numboccur(0,L) = 1
%p end proc:
%p iscyclops(0):= true:
%p select(iscyclops, [seq(n*(3*n-2),n=0..1000)]);
%t 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 *)
%Y Intersection of A000567 and A134808.
%Y Cf. A000567, A134808, A134809, A160717.
%K nonn,base
%O 1,2
%A _K. D. Bajpai_, Apr 25 2017
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