A163236 Inverse permutation to A163235.

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

Offset: 0

Author

Antti Karttunen, Jul 29 2009

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..4095
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

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

Programs

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)<Indranil Ghosh, Jun 25 2017

Scheme

(define (A163236 n) (A001477bi (A006068 (A059906 n)) (A006068 (A059905 n))))
(define (A001477bi x y) (/ (+ (expt (+ x y) 2) x (* 3 y)) 2))

Formula

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