

A176716


a(1) = 1; p(n)*a(n) = a(2n); p(n)*a(n) + a(n+1) = a(2n+1); p(n) = nth 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
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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) = nth prime.
Given the generating triangle of A176528, replace k's with p(k); then take
powers of the triangle resulting in a leftshifted 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 leftshifted 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



