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A279260 Numbers which are cyclops palindromic in their binary reflected Gray code representation. 1
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 (list; graph; refs; listen; history; text; internal format)
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

Cf. A014550, A129868, A134808, A138148.

Sequence in context: A239420 A219590 A260664 * A294471 A194995 A104970

Adjacent sequences:  A279257 A279258 A279259 * A279261 A279262 A279263

KEYWORD

nonn,base,easy

AUTHOR

Indranil Ghosh, Jan 17 2017

STATUS

approved

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Last modified July 27 18:27 EDT 2021. Contains 346308 sequences. (Running on oeis4.)