A279260 Numbers which are cyclops palindromic in their binary reflected Gray code representation.

0, 6, 18, 90, 330, 1386, 5418, 21930, 87210, 349866, 1397418, 5593770, 22366890, 89483946, 357903018, 1431677610, 5726579370, 22906579626, 91625794218, 366504225450, 1466014804650, 5864063412906, 23456245263018, 93824997829290, 375299957762730, 1501199898159786, 6004799458421418

Offset: 0

Author

Indranil Ghosh, Jan 17 2017

Keywords

• nonn
• base
• easy

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.

Examples

			90 is in the sequence because the binary reflected Gray code representation of 90 is '1110111' which is a cyclops palindromic binary number.
		

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)

Crossrefs

Cf. A014550, A129868, A134808, A138148.

Partial sums of A071930.

Programs

PARI

a(n)=(-2*(1+((-2)^n)-(2^(2*n+1))))/3 \\ Charles R Greathouse IV, Jun 29 2018

Python

def a(n):
    return (-2*(1+((-2)**n)-(2**(2*n+1))))/3

Formula

a(n) = (-2*(1+((-2)^n)-(2^(2*n+1))))/3.