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A176716 a(1) = 1; p(n)*a(n) = a(2n); p(n)*a(n) + a(n+1) = a(2n+1); p(n) = n-th prime. 1
1, 2, 4, 6, 10, 20, 26, 42, 52, 110, 130, 260, 286, 442, 484, 798, 850, 1196, 1306, 3190, 3320, 4030, 4290, 9620, 9906 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Conjectures: 4 divides a(n) iff n == 0 mod 3. 2 divides a(n) iff n == (1, 2) mod 3; as the highest power of 2; for n>1.

LINKS

Table of n, a(n) for n=1..25.

FORMULA

a(1) = 1; p(n)*a(n) = a(2n); p(n)*a(n) + a(n+1) = a(2n+1); p(n) = n-th prime.

Given the generating triangle of A176528, replace k's with p(k); then take

powers of the triangle resulting in a left-shifted vector considered as a sequence.

EXAMPLE

First few rows of the generating triangle M for A176716 =

1;

2;

2, 1;

0, 3;

0, 3, 1;

0, 0, 5;

0, 0, 5, 1;

0, 0, 0, 7;

0, 0, 0, 7,. 1;

0, 0, 0, 0, 11;

0, 0, 0, 0, 11,. 1;

0, 0, 0, 0,. 0, 13;

0, 0, 0, 0,. 0, 13,. 1;

0, 0, 0, 0, .0, .0, 17;

...

Then A176716 = Lim_{n->inf} M^n, the left-shifted vector considered as a sequence.

Examples: a(10) = 110 = p(11) * a(5) = 11 * 10.

a(7) = 26 = p(3) * 4 + 6 = 5 * 4 + 6.

4 divides a(9) = 52 since 9 == 0 mod 3

2 divides a(13) = 286 but not 4 since 13 == 1 mod 3.

CROSSREFS

Cf. A176528, A000040

Sequence in context: A034872 A032362 A282251 * A256056 A293281 A164143

Adjacent sequences:  A176713 A176714 A176715 * A176717 A176718 A176719

KEYWORD

nonn

AUTHOR

Gary W. Adamson, Apr 24 2010

STATUS

approved

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Last modified February 20 16:14 EST 2018. Contains 299380 sequences. (Running on oeis4.)