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A334204 a(n) = A329697(A163511(n)). 7
0, 0, 0, 1, 0, 2, 1, 1, 0, 3, 2, 2, 1, 2, 1, 2, 0, 4, 3, 3, 2, 3, 2, 4, 1, 3, 2, 3, 1, 3, 2, 2, 0, 5, 4, 4, 3, 4, 3, 6, 2, 4, 3, 5, 2, 5, 4, 4, 1, 4, 3, 4, 2, 4, 3, 4, 1, 4, 3, 3, 2, 3, 2, 2, 0, 6, 5, 5, 4, 5, 4, 8, 3, 5, 4, 7, 3, 7, 6, 6, 2, 5, 4, 6, 3, 6, 5, 6, 2, 6, 5, 5, 4, 5, 4, 4, 1, 5, 4, 5, 3, 5, 4, 6, 2, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

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

                                     0

                                     |

                  ...................0...................

                 0                                       1

       0......../ \........2                   1......../ \........1

      / \                 / \                 / \                 / \

     /   \               /   \               /   \               /   \

    /     \             /     \             /     \             /     \

   0       3           2       2           1       2           1       2

  0 4     3 3         2 3     2 4         1 3     2 3         1 3     2 2

etc.

The nodes at the left edge are all zeros, and their right-hand children give positive integers, A000027.

Each left-hand leaning branch stays constant, because A329697(2n) = A329697(n).

The right-hand leaning branches are not necessarily monotonic. For example, a((2^6)-1) = 2 > 1 = a((2^7)-1), because A000040(7) = 17 is a Fermat prime (but A000040(6) = 13 is not), and therefore the latter is only one step away from a power of 2.

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..65537

Index entries for sequences related to binary expansion of n

FORMULA

a(n) = A329697(A163511(n)).

a(n) = A334109(A334860(n)).

a(n) = a(2n) = a(A000265(n)).

For all n >= 0, a(2^n) = 0, a(2^n + 1) = n.

PROG

(PARI)

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ From A005940

A054429(n) = ((3<<#binary(n\2))-n-1); \\ From A054429

A163511(n) = if(!n, 1, A005940(1+A054429(n)));

A329697(n) = if(!bitand(n, n-1), 0, 1+A329697(n-(n/vecmax(factor(n)[, 1]))));

A334204(n) = A329697(A163511(n));

CROSSREFS

Cf. A000079, A163511, A329697, A334109, A334860, A334867, A334873.

Sequence in context: A023416 A080791 A336361 * A336362 A336363 A308451

Adjacent sequences:  A334201 A334202 A334203 * A334205 A334206 A334207

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jun 09 2020

STATUS

approved

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Last modified July 27 15:49 EDT 2021. Contains 346308 sequences. (Running on oeis4.)