This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A279260 #42 May 22 2025 10:21:44
%S A279260 0,6,18,90,330,1386,5418,21930,87210,349866,1397418,5593770,22366890,
%T A279260 89483946,357903018,1431677610,5726579370,22906579626,91625794218,
%U A279260 366504225450,1466014804650,5864063412906,23456245263018,93824997829290,375299957762730,1501199898159786,6004799458421418
%N A279260 Numbers which are cyclops palindromic in their binary reflected Gray code representation.
%C A279260 Cyclops palindromic numbers in base 2 are numbers with middle bit 0, having equal number of 1's on both side of the 0. There is a single 0 bit in the middle and the total number of bits is odd. The middle '0' represents the eye of a cyclops.
%C A279260 a(n) mod 6 = 0.
%H A279260 Indranil Ghosh, <a href="/A279260/b279260.txt">Table of n, a(n) for n = 0..1000</a>
%H A279260 Indranil Ghosh, <a href="/A279260/a279260.txt">Proof of 6|{(-2*(1+((-2)^n)-(2^(2*n+1))))/3}</a>
%H A279260 Brady Haran and Simon Pampena, <a href="https://www.youtube.com/watch?v=HPfAnX5blO0">Glitch Primes and Cyclops Numbers</a>, Numberphile video, (2015)
%F A279260 a(n) = (-2*(1+((-2)^n)-(2^(2*n+1))))/3.
%e A279260 90 is in the sequence because the binary reflected Gray code representation of 90 is '1110111' which is a cyclops palindromic binary number.
%o A279260 (Python)
%o A279260 def a(n):
%o A279260 return (-2*(1+((-2)**n)-(2**(2*n+1))))/3
%o A279260 (PARI) a(n)=(-2*(1+((-2)^n)-(2^(2*n+1))))/3 \\ _Charles R Greathouse IV_, Jun 29 2018
%Y A279260 Cf. A014550, A129868, A134808, A138148.
%Y A279260 Partial sums of A071930.
%K A279260 nonn,base,easy
%O A279260 0,2
%A A279260 _Indranil Ghosh_, Jan 17 2017