A246363 - OEIS

%I #9 Aug 27 2014 14:53:07

%S 1,2,4,8,3,9,5,13,10,16,6,14,7,12,35,20,17,79,11,67,71,33,19,271,39,

%T 31,139,87,15,30,18,311,47,34,63,74,23,29,26,351,21,28,27,24,303,69,

%U 25,2431,70,223,135,319,37,1663,65,58,41,38,32,219,43,127,367,327,287,239,55,107,46,283,22,413,51,53,147

%N Permutation of natural numbers: a(n) = A135141(A048673(n)).

%C Apart from 2, even numbers occur only in positions given by A246261 (together with some odd numbers).

%C Also, apart from A246263(1) = 2, the positions given by the rest of A246263: 5, 6, 7, 8, 15, 17, 18, 19, 20, 21, ... contain odd numbers only.

%H Antti Karttunen, <a href="/A246363/b246363.txt">Table of n, a(n) for n = 1..10000</a>

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

%F a(n) = A135141(A048673(n)).

%o (PARI)

%o A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ Using code of _Michel Marcus_

%o A048673(n) = (A003961(n)+1)/2;

%o A135141(n) = if(1==n, 1, if(isprime(n), 2*A135141(primepi(n)), 1+(2*A135141(n-primepi(n)-1))));

%o A246363(n) = A135141(A048673(n));

%o for(n=1, 10000, write("b246363.txt", n, " ", A246363(n)));

%o (Scheme) (define (A246363 n) (A135141 (A048673 n)))

%Y Inverse: A246364.

%Y Related or similar permutations: A048673, A135141, A246365, A246367.

%Y Cf. A000035, A003961, A246260, A246261, A246263.

%K nonn

%O 1,2

%A _Antti Karttunen_, Aug 26 2014