A364297 - OEIS

A364297

a(n) = A348717(A163511(n)).

1, 2, 4, 2, 8, 4, 6, 2, 16, 8, 18, 4, 12, 6, 10, 2, 32, 16, 54, 8, 36, 18, 50, 4, 24, 12, 30, 6, 20, 10, 14, 2, 64, 32, 162, 16, 108, 54, 250, 8, 72, 36, 150, 18, 100, 50, 98, 4, 48, 24, 90, 12, 60, 30, 70, 6, 40, 20, 42, 10, 28, 14, 22, 2, 128, 64, 486, 32, 324, 162, 1250, 16, 216, 108, 750, 54, 500, 250, 686, 8, 144

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

For all i, j: a(i) = a(j) => A278531(i) = A278531(j).

As the underlying sequence A163511 can be represented as a binary tree, so can this be also:

...................2...................

4 2

8......../ \........4 6......../ \........2

/ \ / \ / \ / \

16 8 18 4 12 6 10 2

32 16 54 8 36 18 50 4 24 12 30 6 20 10 14 2

etc.

Each rightward leaning branch stays constant, because a(2n+1) = a(n).

Conjecture: Mersenne primes (A000668) gives all such odd numbers k for which a(k) = A348717(k). If true, then it immediately implies that map n -> A163511(n) [or equally: map n -> A243071(n)] has no other fixed points than those given by A007283. But see also A364959. - Edited Sep 03 2023

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..8192

Index entries for sequences related to binary expansion of n

Index entries for sequences computed from indices in prime factorization

FORMULA

a(0) = 1, a(1) = 2, a(2n) = A163511(2n) = 2*A163511(n), and for n > 0, a(2n+1) = a(n).

PROG

(PARI)

A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));

A348717(n) = if(1==n, 1, my(f = factor(n), k = primepi(f[1, 1])-1); for (i=1, #f~, f[i, 1] = prime(primepi(f[i, 1])-k)); factorback(f));

A364297(n) = A348717(A163511(n));

CROSSREFS