A245608 Permutation of natural numbers, the even bisection of A245606 halved: a(n) = A245606(2*n)/2.

1, 2, 3, 5, 4, 8, 13, 11, 6, 14, 18, 41, 7, 26, 28, 20, 9, 23, 63, 50, 25, 113, 313, 65, 12, 17, 88, 77, 172, 149, 43, 95, 16, 38, 33, 44, 10, 413, 163, 221, 19, 74, 48, 191, 22, 476, 118, 179, 49, 68, 138, 29, 39, 527, 78, 215, 31, 635, 1593, 227, 102, 71, 688, 242, 24, 122, 193, 104, 15, 98, 58, 176, 30, 32, 123

Offset: 1

Author

Antti Karttunen, Jul 29 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: A245607.

Cf. A003961, A048673, A245606, A245609-A245610, A245706, A245708, A245709, A245612, A244154, A243065-A243066.

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))))
A245608(n) = A245606(2*n)/2;
for(n=1, 10001, write("b245608.txt", n, " ", A245608(n)))

Scheme

(define (A245608 n) (A048673 (A245606 n)))

Formula

a(n) = A245606(2*n)/2.

As a composition of related permutations:

a(n) = A048673(A245606(n)).

a(n) = A245708(A245706(n)).

Other identities:

For all n >= 0, a(2^n) = A245708(2^n). Moreover, A245709 gives all such k that a(k) = A245708(k).