cp's OEIS Frontend

A332214 Mersenne-prime fixing variant of permutation A163511: a(n) = A332212(A163511(n)).

%I A332214 #26 Oct 12 2023 16:59:33
%S A332214 1,2,4,3,8,9,6,7,16,27,18,49,12,21,14,5,32,81,54,343,36,147,98,25,24,
%T A332214 63,42,35,28,15,10,31,64,243,162,2401,108,1029,686,125,72,441,294,175,
%U A332214 196,75,50,961,48,189,126,245,84,105,70,155,56,45,30,217,20,93,62,11,128,729,486,16807,324,7203,4802,625,216,3087,2058,875
%N A332214 Mersenne-prime fixing variant of permutation A163511: a(n) = A332212(A163511(n)).
%C A332214 Any Mersenne prime (A000668) times any power of 2, i.e., sequence A335431, is fixed by this map (note the indexing), including also all even perfect numbers. It is not currently known whether there are any additional fixed points.
%C A332214 Because a(n) has the same prime signature as A163511(n), it implies that applying A046523 and A052409 to this sequence gives the same results as with A163511, namely, sequences A278531 and A365805. - _Antti Karttunen_, Oct 09 2023
%H A332214 Antti Karttunen, <a href="/A332214/b332214.txt">Table of n, a(n) for n = 0..8191</a>
%H A332214 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A332214 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A332214 a(n) = A332212(A163511(n)).
%o A332214 (PARI) A332214(n) = A332212(A163511(n));
%o A332214 (PARI)
%o A332214 \\ Needs precomputed data for A332211:
%o A332214 v332211 = readvec("b332211_to.txt"); \\ Prepared with gawk ' { print $2 } ' < b332211.txt > b332211_to.txt
%o A332214 A332211(n) = v332211[n];
%o A332214 A332214(n) = if(!n, 1, my(i=1, p=A332211(i), t=1); while(n>1, if(!(n%2), (t*=p), i++; p=A332211(i)); n >>= 1); (t*p)); \\ _Antti Karttunen_, Oct 09 2023
%Y A332214 Cf. A163511, A332211, A332212, A332215 (inverse permutation).
%Y A332214 Cf. A278531 [= A046523(a(n))], A290251 [= A001222(a(n))], A365805 [= A052409(a(n))], A366372 [= a(n)-n], A366373 [= gcd(n,a(n))], A366374 (numerator of n/a(n)), A366375 (denominator of n/a(n)), A366376.
%Y A332214 Cf. A000043, A000668, A000396, A324200, A335431 (conjectured to give all the fixed points).
%K A332214 nonn,look
%O A332214 0,2
%A A332214 _Antti Karttunen_, Feb 09 2020