A104772 If n<=2 then n else (if n is odd then 2*a(n+1) else p*q, where n=p+q, p<=q, primes).

1, 2, 8, 4, 18, 9, 30, 15, 42, 21, 70, 35, 66, 33, 78, 39, 130, 65, 102, 51, 114, 57, 190, 95, 138, 69, 230, 115, 322, 161, 174, 87, 186, 93, 310, 155, 434, 217, 222, 111, 370, 185, 246, 123, 258, 129, 430, 215, 282, 141, 470, 235, 658, 329, 318, 159, 530, 265, 742

Offset

1,2

Comments

Encoding of positive integers based on the Goldbach conjecture, see A104774 for decoding: A104774(A104772(n))=n;

a(n - n mod 2) = (2^(1 + n mod 2)) * A020481(floor(n/2))*A020482(floor(n/2));

for numbers greater than 4: a(even) = odd and a(odd) = even;

A001222(a(n)) = A010693(n) for n>2;

a(a(n)) = A104773(n).

Links

Table of n, a(n) for n=1..59.

Index entries for sequences related to Goldbach conjecture

Formula

For k>1: a(2*k)=A020481(k)*A020482(k) and a(2*k-1)=2*a(2*k).

Crossrefs

Cf. A001358, A046315, A090967.

Sequence in context: A175181 A110003 A035302 * A264142 A088156 A019193

Adjacent sequences: A104769 A104770 A104771 * A104773 A104774 A104775

Keyword

nonn

Author

Reinhard Zumkeller, Mar 24 2005

Status

approved