%I #13 Jun 24 2024 22:27:33

%S 1,3,6,13,27,55,110,220,441,883,1766,3532,7064,14129,28258,56517,

%T 113035,226070,452140,904281,1808562,3617124,7234249,14468499,

%U 28936999,57873998,115747997,231495994,462991989,925983979,1851967959,3703935918

%N Binary representation of a(n) equals first n+1 terms of A051023.

%C a(n+1) = 2*a(n) + d, where d = 0/1 with no obvious rule. The sequence is a digit representation of the central column of cellular automaton Rule 30, A051023. Primes in the sequence, A092540.

%H Reinhard Zumkeller, <a href="/A092539/b092539.txt">Table of n, a(n) for n = 0..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Rule30.html">Rule 30</a>.

%F a(n+1) = 2*a(n) + A051023(n+1). - _Reinhard Zumkeller_, Jun 08 2013

%e a(6) = 55_10 = 110111_2

%t a(n_) := FromDigits[Take[A051023, n], 2]

%o (Haskell)

%o a092539 n = a092539_list !! n

%o a092539_list = scanl1 (\v d -> 2 * v + d) $ map toInteger a051023_list

%o -- _Reinhard Zumkeller_, Jun 08 2013

%Y Cf. A051023, A092540.

%K easy,nonn

%O 0,2

%A _Zak Seidov_, Feb 27 2004

%E Offset corrected and definition adjusted by _Reinhard Zumkeller_, Jun 08 2013