A049821 a(n) = j + k, where u(n) = u(j) + u(k) is the unique sum of Ulam numbers described in A002859 (with 1 <= j < k < n).

3, 4, 5, 6, 8, 9, 12, 12, 14, 15, 15, 17, 18, 18, 20, 20, 22, 23, 23, 25, 25, 27, 28, 28, 35, 28, 29, 35, 33, 38, 35, 41, 37, 37, 39, 41, 46, 48, 43, 51, 45, 53, 48, 48, 50, 50, 58, 52, 60, 54, 56, 62, 56, 65, 59, 61, 61, 63, 70, 64, 66, 71, 66, 73, 69, 77, 71, 79, 73, 83, 74, 76, 78

Offset: 3

Author

Clark Kimberling

Keywords

• nonn

Examples

			From _Petros Hadjicostas_, Nov 20 2019: (Start)
A002859(3) = 4 = 1 + 3 = A002859(1) + A002859(2), so a(3) = 1 + 2 = 3.
A002859(4) = 5 = 1 + 4 = A002859(1) + A002859(3), so a(4) = 1 + 3 = 4.
A002859(5) = 6 = 1 + 5 = A002859(1) + A002859(4), so a(5) = 1 + 4 = 5.
A002859(6) = 8 = 3 + 5 = A002859(2) + A002859(4), so a(6) = 2 + 4 = 6.
A002859(7) = 10 = 4 + 6 = A002859(3) + A002859(5), so a(7) = 3 + 5 = 8.
(End)
		

Links

• Eric Weisstein's World of Mathematics, Ulam Sequence.
• Wikipedia, Ulam number.

Crossrefs

Cf. A002858, A002859, A049877, A049878, A049879.

Programs

Maple

# First we modify Peter Luschny's program from A002858 (with len >= 3):
UlamList := proc(len) local isUlam, nextUlam, behead; behead := u -> u[2 .. numelems(u)]; isUlam := proc(n, h, u, r) local hu, tu, hr, tr; hu := u[1]; hr := r[1]; if h = 2 then return false; end if; if hr <= hu then return evalb(h = 1); end if; if hr + hu = n then tu := behead(u); tr := behead(r); return isUlam(n, h + 1, tu, tr); end if; if hr + hu < n then tu := behead(u); return isUlam(n, h, tu, r); end if; tr := behead(r); isUlam(n, h, u, tr); end proc; nextUlam := proc(n, u, r) if isUlam(n, 0, u, r) then if nops(u) = len - 1 then return [op(u), n]; end if; nextUlam(n + 1, [op(u), n], [n, op(r)]); else nextUlam(n + 1, u, r); end if; end proc; nextUlam(3, [1, 3], [3, 1]); end proc:
# Next we create a function to calculate a(n) for given n >= 3:
a := proc(n) local u, a, i, j: u := 0: if 3 <= n then a := UlamList(n): for i to n - 2 do for j from i + 1 to n - 1 do if a[n] = a[i] + a[j] then u := i+j: end if: end do: end do: end if: u: end proc:
# Finally, we create a list of values for a(n):
seq(a(n), n=3..100); # Petros Hadjicostas, Nov 20 2019

Extensions

Name edited by and typo in the data corrected by Petros Hadjicostas, Nov 20 2019

More terms from Petros Hadjicostas, Nov 20 2019