A285767 Cyclops octagonal numbers: a(n) = n*(3*n-2) with one "zero" digit in the middle.

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

Offset: 1

Author

K. D. Bajpai, Apr 25 2017

Keywords

• nonn
• base

Comments

The n-th octagonal number x(n) = n*(3*n - 2).

Subset of A000567.

All the terms have the number of digits odd with only one "zero" digit in the middle.

Examples

			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.
		

Crossrefs

Intersection of A000567 and A134808.

Cf. A000567, A134808, A134809, A160717.

Programs

Maple

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)]);

Mathematica

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 *)