A086772 Store the natural numbers in a triangular array such that values on each row have the same number of bits. Start a new row with the smallest number not yet recorded. a(n) represents the initial terms in the resulting array.

0, 1, 3, 4, 7, 9, 15, 21, 24, 31, 41, 45, 63, 64, 72, 74, 83, 94, 127, 139, 140, 173, 197, 207, 234, 255, 268, 284, 288, 339, 349, 390, 426, 445, 467, 511, 522, 553, 569, 634, 689, 706, 734, 797, 838, 934, 950, 951, 1023, 1036, 1052, 1078, 1179, 1236

Offset: 0

Author

Alford Arnold, Aug 03 2003

Keywords

• nonn
• base

Comments

A067576 describes the sequences with a fixed number of binary bits using antidiagonals.

Examples

			The array begins:
   0
   1  2
   3  5  6
   4  8 16 32
   7 11 13 14 19
   9 10 12 17 18 20
  15 23 27 29 30 39 43
  ...
so the initial terms are 0 1 3 4 7 9 15 ...
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000079, A001477, A018900, A014311, A014312, A014313, A023688, A023689, A023690, A023691.

Programs

Maple

A086772aux := proc(n,k)
    option remember;
    local a,npr,kpr,fnd ;
    if n = 0 then
        return 0;
    end if;
    if k = 0 then
        for a from 1 do
            fnd := false;
            for npr from 1 to n-1 do
                for kpr from 0 to npr do
                    if procname(npr,kpr) = a then
                        fnd := true;
                        break;
                    end if;
                end do:
            end do:
            if not fnd then
                return a;
            end if;
        end do:
    else
        for a from 1 do
            if wt(a) = wt(procname(n,0)) then
                fnd := false;
                for npr from 1 to n-1 do
                    for kpr from 0 to npr do
                        if procname(npr,kpr) = a then
                            fnd := true;
                            break;
                        end if;
                    end do:
                end do:
                for kpr from 0 to k-1 do
                    if procname(n,kpr) = a then
                        fnd := true;
                        break;
                    end if;
                end do:
                if not fnd then
                    return a;
                end if;
            end if;
        end do:
    end if;
end proc:
A086772 := proc(n)
    A086772aux(n,0) ;
end proc: # R. J. Mathar, Sep 15 2012