A094077

[Klaus Brockhaus]

Apparently

A001951 a(n) = floor[n*sqrt 2], 	(1, 2, 4, 5, 7, 8, 9, 11, 12, 14, 15, 16, 18, ...)

and

A001952: a(n) = floor[n*(2 + sqrt 2)], (3, 6, 10, 13, 17, 20, 23, 27, 30, 34, 37, 40, 44, ...)

are the bisection of

A094077: a(1)=1 and, for n>1, a(n)=a(n-1)+n if n is even, and a(n)=smallest positive integer which has not yet appeared in the sequence if n is odd, (1, 3, 2, 6, 4, 10, 5, 13, 7, 17, 8, 20, 9, 23, 11, 27, 12, 30, 14, 34, 15, 37, 16, 40, 18, 44, ...).

>From the definitions this is by no means obvious, but perhaps someone has an idea how it can be proved.

Thanks,
Klaus