A293517 a(n) = A293518(n) - A293519(n); how many more surviving even nodes than surviving (but not bifurcating) odd nodes there are at generation n in the binary tree of persistently squarefree numbers.

0, 1, 1, 1, 1, 2, 1, 3, 4, 5, 9, 8, 10, 20, 17, 36, 32, 50, 66, 83, 118, 171, 219, 291, 410, 511, 730, 952, 1325, 1665, 2389, 3100, 4147, 5631, 7591, 10093, 13756, 18390, 24540, 33288, 44391, 60052, 80291, 108096, 145226, 194764, 262091, 352096, 473452, 635336, 854332, 1147668

Offset

0,6

Comments

As long as there are at least as many surviving even than surviving (but not bifurcating) odd nodes at each generation in the tree of persistently squarefree numbers (see illustration in A293230), this sequence also stays nonnegative, and being also the first differences of A293441 guarantees its monotonicity. If A293441 is monotonic, then A293230 is also, which in turn implies also that A293430 has infinite number of terms and that there will be nonzero terms arbitrary far in A293233.

The surviving children of even vertices are all of the form 4k+1, while the surviving children (those without an odd sibling) of odd vertices are all of the form 4k+2.

Links

Table of n, a(n) for n=0..51.

Formula

a(n) = A293518(n) - A293519(n).

a(n) = A293441(1+n) - A293441(n).

Prog

(Scheme) (define (A293517 n) (- (A293518 n) (A293519 n)))

Crossrefs

Cf. A293230, A293233, A293430, A293518, A293519.

First differences of A293441.

Cf. also A293428.

Sequence in context: A075379 A308000 A029636 * A122514 A130077 A080412

Adjacent sequences: A293514 A293515 A293516 * A293518 A293519 A293520

Keyword

nonn

Author

Antti Karttunen, Oct 16 2017

Status

approved