A129674 - OEIS

%I #11 Jul 22 2020 11:46:55

%S 3,2,1,6,4,7,5,10,8,12,11,13,15,14,9,18,16,20,19,21,17,24,22,25,27,26,

%T 23,30,28,31,29,34,32,36,35,37,33,40,38,41,43,42,39,46,44,48,47,49,51,

%U 50,45,54,52,55,53,58,56,60,59,61,63,62,57,66,64,68,67,69,65,72,70,73

%N Permutation sequence generated by the "evil numbers" (A001969), by swapping n-th natural number by the (n-g)-th sequentially (iteratively), where g=min(evil(n+1)-evil(n)-1,n-1).

%C In contrast to A128754 and A128756 (which are generated analogously from the primes and the lucky numbers, respectively), this sequence seems consisting solely of fixed points and cycles of length 4, 5 and 6 (apart from the initial cycle of length 2). It is also notable that the difference of the number of fixed points and the number of cycles never differs by more than 4, up to index 10000, according to numerical tests. Thus the ratio of the number of fixed points to the number of cycles seems to be asymptotically equal to unity.

%H Ferenc Adorjan, <a href="/A129674/b129674.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>

%o (PARI) {vperm(z)=local(n,m,q,v,x,j,g);

%o /* Permutation of positive integers so that starting with the sequence of positive integers, sequentially swap the i-th term with max(i-g(i),1)-th term, where g(i)=z[i+1]-z[i]-1. */

%o j=matsize(z)[2]-1;n=j-z[j]+z[j-6];v=vector(j);x=vector(n);for(i=1,j,v[i]=i);

%o for(i=1,j,g=min(z[i+1]-z[i]-1,i-1);q=v[i];v[i]=v[i-g];v[i-g]=q);for(i=1,n,x[i]=v[i]);return(x)}

%o a=vperm(A001969)

%Y Inverse of A129675, Cf. A128754, A128756, A129676, A129677, A129678 and A001969.

%K nonn,base

%O 1,1

%A Ferenc Adorjan (fadorjan(AT)freemail.hu or ferencadorjan(AT)gmail.com), May 01 2007