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

1,2

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.

Links

Table of n, a(n) for n=1..32.

Example

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.

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 *)

Crossrefs

Intersection of A000567 and A134808.

Cf. A000567, A134808, A134809, A160717.

Sequence in context: A234697 A337795 A183717 * A282479 A163024 A283948

Adjacent sequences: A285764 A285765 A285766 * A285768 A285769 A285770

Keyword

nonn,base

Author

K. D. Bajpai, Apr 25 2017

Status

approved