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A163236 Inverse permutation of A163235. 4
0, 2, 1, 4, 9, 5, 13, 8, 6, 11, 3, 7, 24, 17, 18, 12, 35, 27, 43, 34, 14, 20, 19, 26, 62, 51, 52, 42, 32, 41, 25, 33, 28, 37, 21, 29, 58, 47, 48, 38, 10, 16, 15, 22, 31, 23, 39, 30, 112, 97, 98, 84, 70, 83, 59, 71, 73, 61, 85, 72, 40, 50, 49, 60, 135, 119, 151, 134, 90 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..4095

Index entries for sequences that are permutations of the natural numbers

FORMULA

a(n) = A001477bi(A006068(A059906(n)),A006068(A059905(n))), where A001477bi(x,y) = (((x+y)^2)+x+(3y))/2.

PROG

(Scheme:) (define (A163236 n) (A001477bi (A006068 (A059906 n)) (A006068 (A059905 n))))

(define (A001477bi x y) (/ (+ (expt (+ x y) 2) x (* 3 y)) 2))

(Python)

def A(x, y): return (((x + y)**2) + x + 3*y)//2

def a006068(n):

    s=1

    while True:

        ns=n>>s

        if ns==0: break

        n=n^ns

        s<<=1

    return n

def a059905(n): return sum([(n>>2*i&1)<<i for i in range(int(len(bin(n)[2:])//2) + 1)])

def a059906(n):

    x=[int(k) for k in list(bin(n)[2:])][::-1]

    return sum([x[2*i + 1]*2**i for i in range(len(x)//2)])

def a(n): return A(a006068(a059906(n)), a006068(a059905(n)))

print([a(n) for n in range(101)]) # Indranil Ghosh, Jun 25 2017

CROSSREFS

Inverse: A163235. a(n) = A163234(A057300(n)). Cf. A163234.

Sequence in context: A086933 A077878 A128058 * A325008 A325016 A077160

Adjacent sequences:  A163233 A163234 A163235 * A163237 A163238 A163239

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jul 29 2009

STATUS

approved

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Last modified June 23 21:09 EDT 2021. Contains 345402 sequences. (Running on oeis4.)