A245708 Permutation of natural numbers, the odd bisection of A245606 incremented by one and halved: a(n) = (1+A245606((2*n)-1))/2.

1, 2, 3, 5, 4, 8, 6, 11, 7, 14, 13, 41, 10, 23, 63, 20, 15, 17, 9, 50, 16, 26, 21, 65, 45, 32, 18, 44, 30, 413, 58, 95, 22, 53, 12, 29, 27, 38, 66, 221, 52, 122, 48, 77, 115, 83, 748, 179, 69, 263, 25, 365, 39, 113, 153, 176, 130, 158, 508, 1007, 247, 140, 78, 242, 97, 59, 33, 89, 72, 68, 36, 47, 49, 188, 28

Offset: 1

Author

Antti Karttunen, Jul 30 2014

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10001
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse: A245707.

Cf. A003961, A048673, A245606, A245608, A245705, A245709.

Programs

PARI

A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ This function from Michel Marcus
A245606(n) = if(1==n, 1, if(0==(n%2), 1+A003961(A245606(n/2)), A003961(1+A245606((n-1)/2))));
A245708(n) = (1+A245606((2*n)-1))/2;
for(n=1, 10001, write("b245708.txt", n, " ", A245708(n)))

Scheme

(define (A245708 n) (* (/ 1 2) (+ 1 (A245606 (-1+ (* 2 n))))))

Scheme

(define (A245708 n) (if (= 1 n) n (A048673 (+ 1 (A245606 (- n 1))))))

Formula

a(n) = (1+A245606((2*n)-1))/2.

As a composition of related permutations:

a(1) = 1, and for n > 1, a(n) = A048673(1+A245606(n-1)).

a(n) = A245608(A245705(n)).

Other identities:

For all n >= 0, a(2^n) = A245608(2^n). Moreover, A245709 gives all such k that a(k) = A245608(k).