A245608 - OEIS

%I #17 Jul 31 2014 23:50:09

%S 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,

%T 17,88,77,172,149,43,95,16,38,33,44,10,413,163,221,19,74,48,191,22,

%U 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

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

%H Antti Karttunen, <a href="/A245608/b245608.txt">Table of n, a(n) for n = 1..10001</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

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

%F As a composition of related permutations:

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

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

%F Other identities:

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

%o (PARI)

%o 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_

%o A245606(n) = if(1==n, 1, if(0==(n%2), 1+A003961(A245606(n/2)),A003961(1+A245606((n-1)/2))))

%o A245608(n) = A245606(2*n)/2;

%o for(n=1, 10001, write("b245608.txt", n, " ", A245608(n)))

%o (Scheme) (define (A245608 n) (A048673 (A245606 n)))

%Y Inverse: A245607.

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

%K nonn

%O 1,2

%A _Antti Karttunen_, Jul 29 2014