OFFSET
0,2
COMMENTS
Or a(n) is in A145812 such that (2*n + 3 - a(n))/2 is in A145812 as well. Note also that a(n) + 2*A090569(n+1) = 2*n + 3. - Vladimir Shevelev, Oct 20 2008
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
C. Groer, The Mathematics of Survival: From Antiquity to the Playground, Amer. Math. Monthly, 110 (No. 9, 2003), 812-825. (This is the sequence W(2n+1).)
FORMULA
To get a(n), write 2n+1 as Sum b_j 2^j, then a(n) = 1 + Sum_{j odd} b_j 2^j.
Equals A004514(n) + 1. - Chris Groer (cgroer(AT)math.uga.edu), Nov 10 2003
a(n) = 2*A063694(n) + 1. - G. C. Greubel, Dec 05 2022
EXAMPLE
If n=4, 2n+1 = 9 = 1 + 0*2 + 0*2^2 + 1*2^3, so a(4) = 1 + 0*2 + 1*2^3 = 9.
MAPLE
a:=proc(n) local b: b:=convert(2*n+1, base, 2): 1+sum(b[2*j]*2^(2*j-1), j=1..nops(b)/2) end: seq(a(n), n=0..100);
with(Bits): seq(And(2*n+1, convert("aaaaaa", decimal, hex)) + 1, n=0..127); # Georg Fischer, Dec 03 2022
MATHEMATICA
PROG
(Haskell)
a088442 = (+ 1) . a004514 -- Reinhard Zumkeller, Sep 26 2015
(Magma)
function A063694(n)
if n le 1 then return n;
else return 4*A063694(Floor(n/4)) + (n mod 2);
end if; return A063694;
end function;
[A088442(n): n in [0..100]]; // G. C. Greubel, Dec 05 2022
(SageMath)
def A063694(n):
if (n<2): return n
else: return 4*A063694(floor(n/4)) + (n%2)
[A088442(n) for n in range(101)] # G. C. Greubel, Dec 05 2022
(Python)
def A088442(n): return ((n&((1<<(m:=n.bit_length())+(m&1))-1)//3)<<1)+1 # Chai Wah Wu, Jan 30 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Nov 09 2003
EXTENSIONS
More terms from Emeric Deutsch, May 27 2004
STATUS
approved