A049877 a(n) = max(j,k), where u(n) = u(j) + u(k) is the unique sum of Ulam numbers described in A002859 (with 1 <= j < k < n).

2, 3, 4, 4, 5, 6, 8, 9, 9, 11, 12, 12, 14, 15, 16, 17, 17, 19, 20, 21, 22, 22, 24, 25, 20, 27, 27, 27, 30, 27, 32, 27, 34, 35, 36, 36, 27, 27, 40, 27, 42, 36, 44, 45, 46, 47, 31, 49, 33, 51, 52, 35, 53, 38, 56, 57, 58, 58, 43, 61, 62, 44, 63, 46, 66, 50, 68, 52, 70, 47, 72, 73, 73, 60

Offset

3,1

Links

Table of n, a(n) for n=3..76.

Eric Weisstein's World of Mathematics, Ulam Sequence.

Wikipedia, Ulam number.

Example

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

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 := max(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

Crossrefs

Cf. A002858, A002859, A049821, A049878, A049879.

Sequence in context: A317143 A351520 A065328 * A029063 A015737 A015745

Adjacent sequences: A049874 A049875 A049876 * A049878 A049879 A049880

Keyword

nonn

Author

Clark Kimberling

Extensions

Name edited by and more terms from Petros Hadjicostas, Nov 20 2019

Status

approved