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A323505 Mirror image of (denominators of) Bernoulli tree, A106831. 9
1, 2, 4, 6, 8, 12, 12, 24, 16, 24, 24, 48, 24, 36, 48, 120, 32, 48, 48, 96, 48, 72, 96, 240, 48, 72, 72, 144, 96, 144, 240, 720, 64, 96, 96, 192, 96, 144, 192, 480, 96, 144, 144, 288, 192, 288, 480, 1440, 96, 144, 144, 288, 144, 216, 288, 720, 192, 288, 288, 576, 480, 720, 1440, 5040, 128, 192, 192, 384, 192, 288, 384, 960, 192, 288, 288 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

In contrast to A106831 which follows Woon's original indexing (and orientation), this variant starts with value a(0) = 1, with the rest of terms having an index incremented by one, thus allowing for a simple recurrence.

Sequence contains only terms of A001013 and each a(n) is a multiple of A246660(n).

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..16383

S. C. Woon, A tree for generating Bernoulli numbers, Math. Mag., 70 (1997), 51-56.

Index entries for sequences related to Bernoulli numbers.

FORMULA

a(0) = 1; and for n > 0, if n is even, a(n) = 2*a(n/2), and if n is odd, a(n) = (A001511(n+1)+1-A036987(n)) * a((n-1)/2).

For n > 0, a(n) = b(A054429(n)), where b(n) = A106831(n-1).

a(n) = A246660(n) * A323506(n).

a(n) = A323508(A005940(1+n)).

EXAMPLE

This sequence can be represented as a binary tree:

1

|

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

4 6

8......../ \........12 12........./ \.......24

/ \ / \ / \ / \

/ \ / \ / \ / \

/ \ / \ / \ / \

16 24 24 48 24 36 48 120

32 48 48 96 48 72 96 240 48 72 72 144 96 144 240 720

etc.

PROG

(PARI)

A001511(n) = (1+valuation(n, 2));

A036987(n) = !bitand(n, 1+n);

A323505(n) = if(!n, 1, if(!(n%2), 2*A323505(n/2), (A001511(n+1)+1-A036987(n))*A323505((n-1)/2)));

(PARI)

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

A106831r1(n) = if(!n, 1, if(n%2, 2*A106831r1((n-1)/2), (1+A001511(n))*A106831r1(n/2))); \\ Recurrence for A106831, when prepended with 1, thus shifted one term right

A323505(n) = A106831r1(A054429(n));

CROSSREFS

Cf. A000079 (left edge), A000142 (right edge), A001013, A001511, A036987, A054429, A246660, A323506, A323508.

Cf. A106831 and also A005940, A283477, A322827 for other similar trees.

Sequence in context: A028328 A274262 A092990 * A350355 A172311 A103829

Adjacent sequences: A323502 A323503 A323504 * A323506 A323507 A323508

KEYWORD

nonn,tabf

AUTHOR

Antti Karttunen, Jan 16 2019

STATUS

approved

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Last modified February 5 03:48 EST 2023. Contains 360082 sequences. (Running on oeis4.)