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

%I A245708 #14 Mar 27 2025 21:32:05
%S A245708 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,
%T A245708 18,44,30,413,58,95,22,53,12,29,27,38,66,221,52,122,48,77,115,83,748,
%U A245708 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
%N A245708 Permutation of natural numbers, the odd bisection of A245606 incremented by one and halved: a(n) = (1+A245606((2*n)-1))/2.
%H A245708 Antti Karttunen, <a href="/A245708/b245708.txt">Table of n, a(n) for n = 1..10001</a>
%H A245708 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A245708 a(n) = (1+A245606((2*n)-1))/2.
%F A245708 As a composition of related permutations:
%F A245708 a(1) = 1, and for n > 1, a(n) = A048673(1+A245606(n-1)).
%F A245708 a(n) = A245608(A245705(n)).
%F A245708 Other identities:
%F A245708 For all n >= 0, a(2^n) = A245608(2^n). Moreover, A245709 gives all such k that a(k) = A245608(k).
%o A245708 (PARI)
%o A245708 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 A245708 A245606(n) = if(1==n, 1, if(0==(n%2), 1+A003961(A245606(n/2)), A003961(1+A245606((n-1)/2))));
%o A245708 A245708(n) = (1+A245606((2*n)-1))/2;
%o A245708 for(n=1, 10001, write("b245708.txt", n, " ", A245708(n)))
%o A245708 (Scheme)
%o A245708 (define (A245708 n) (* (/ 1 2) (+ 1 (A245606 (-1+ (* 2 n))))))
%o A245708 (Scheme)
%o A245708 (define (A245708 n) (if (= 1 n) n (A048673 (+ 1 (A245606 (- n 1))))))
%Y A245708 Inverse: A245707.
%Y A245708 Cf. A003961, A048673, A245606, A245608, A245705, A245709.
%K A245708 nonn
%O A245708 1,2
%A A245708 _Antti Karttunen_, Jul 30 2014