A145819 Union of A145812 and A145818 with double repetition of 1, so that a(1)=1, a(2)=1

1, 1, 3, 5, 9, 11, 17, 21, 33, 35, 41, 43, 65, 69, 81, 85, 129, 131, 137, 139, 161, 163, 169, 171, 257, 261, 273, 277, 321, 325, 337, 341

Offset

1,3

Comments

Theorem. For every even integer m there exists a representation of the form m=a(r)+a(s). If A(x) is the counting function of a(n)<=x, then A(x)=O(sqrt(x))and Omega(sqrt(x)). Conjecture. The sequence is minimal in the following sense: if any sequence has the counting function B(x)<=A(x) for all x>=1 and B(x) < A(x) for x>=x_0, then there exists an even integer N which is not expressible as a sum of two terms of such sequence.

Links

Table of n, a(n) for n=1..32.

Crossrefs

Cf. A145812, A145818.

Sequence in context: A138203 A225523 A007952 * A317827 A296768 A302596

Adjacent sequences: A145816 A145817 A145818 * A145820 A145821 A145822

Keyword

nonn

Author

Vladimir Shevelev, Oct 20 2008

Status

approved