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

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, 63, 42, 35, 28, 15, 10, 31, 64, 243, 162, 2401, 108, 1029, 686, 125, 72, 441, 294, 175, 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

Offset

0,2

Comments

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.

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

Links

Antti Karttunen, Table of n, a(n) for n = 0..8191

Index entries for sequences related to binary expansion of n

Index entries for sequences that are permutations of the natural numbers

Formula

a(n) = A332212(A163511(n)).

Prog

(PARI) A332214(n) = A332212(A163511(n));
(PARI)
\\ Needs precomputed data for A332211:
v332211 = readvec("b332211_to.txt"); \\ Prepared with gawk ' { print $2 } ' < b332211.txt > b332211_to.txt
A332211(n) = v332211[n];
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

Crossrefs

Cf. A163511, A332211, A332212, A332215 (inverse permutation).

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.

Cf. A000043, A000668, A000396, A324200, A335431 (conjectured to give all the fixed points).

Sequence in context: A366275 A163511 A332817 * A285322 A129593 A338619

Adjacent sequences: A332211 A332212 A332213 * A332215 A332216 A332217

Keyword

nonn,look

Author

Antti Karttunen, Feb 09 2020

Status

approved