1,3

Using the terminology of A008932, call a set A a basis of order h if every

number can be written as the sum of h (not necesarily distinct) elements of

A. Call a basis an increasing basis of order h if its elements are arranged

in increasing order, a0<a1<a2<...

This sequence is made as follows: Take the union of the following three

sets: (1) the set of all nonnegative numbers which can be written in base

two as sums of powers, k, of 2, where k is congruent to 0 mod 3; (2) the set

of all nonnegative numbers which can be written in base two as sums of

powers, k, of 2, where k is congruent to 1 mod 3; (3) the set of all

nonnegative numbers which can be written in base tow as sums of powers, k,

of 2, where k is congruent to 2 mod 3.

Numbers of the form A033045(k), or 2*A033045(k), or 4*A033045(k). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 21 2009]

ismod3 := proc(n, m) b := convert(n, base, 2) ; for i from 1+((m+1) mod 3) to nops(b) by 3 do if op(i, b) <> 0 then RETURN(false) ; fi; od: for i from 1 + ((m+2) mod 3) to nops(b) by 3 do if op(i, b) <> 0 then RETURN(false) ; fi; od: true ; end: for n from 0 to 20700 do if ismod3(n, 0) or ismod3(n, 1) or ismod3(n, 2) then printf("%d, ", n); fi; od: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 21 2009]

Cf. A008932, A152112.

Sequence in context: A023898 A125853 A080025 this_sequence A025611 A049439 A079931

Adjacent sequences: A152108 A152109 A152110 this_sequence A152112 A152113 A152114

nonn,easy

David Newman (davidsnewman(AT)gmail.com), Mar 22 2009

More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 21 2009