OFFSET
0,2
COMMENTS
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.
a(n) mod 6 = 0.
LINKS
Indranil Ghosh, Table of n, a(n) for n = 0..1000
Indranil Ghosh, Proof of 6|{(-2*(1+((-2)^n)-(2^(2*n+1))))/3}
Brady Haran and Simon Pampena, Glitch Primes and Cyclops Numbers, Numberphile video, (2015)
FORMULA
a(n) = (-2*(1+((-2)^n)-(2^(2*n+1))))/3.
EXAMPLE
90 is in the sequence because the binary reflected Gray code representation of 90 is '1110111' which is a cyclops palindromic binary number.
PROG
(Python)
def a(n):
....return (-2*(1+((-2)**n)-(2**(2*n+1))))/3
(PARI) a(n)=(-2*(1+((-2)^n)-(2^(2*n+1))))/3 \\ Charles R Greathouse IV, Jun 29 2018
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Indranil Ghosh, Jan 17 2017
STATUS
approved