A049878 a(n) = min(j,k), where u(n) = u(j) + u(k) is the unique sum of Ulam numbers described in A002859 (with 1 <= j < k < n).

1, 1, 1, 2, 3, 3, 4, 3, 5, 4, 3, 5, 4, 3, 4, 3, 5, 4, 3, 4, 3, 5, 4, 3, 15, 1, 2, 8, 3, 11, 3, 14, 3, 2, 3, 5, 19, 21, 3, 24, 3, 17, 4, 3, 4, 3, 27, 3, 27, 3, 4, 27, 3, 27, 3, 4, 3, 5, 27, 3, 4, 27, 3, 27, 3, 27, 3, 27, 3, 36, 2, 3, 5, 27, 14, 27, 3, 27, 3, 27, 3, 4, 3, 27, 3, 4, 27, 3

Offset

3,4

Links

Table of n, a(n) for n=3..90.

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) = min(1,2) = 1.
A002859(4) = 5 = 1 + 4 = A002859(1) + A002859(3), so a(4) = min(1,3) = 1.
A002859(5) = 6 = 1 + 5 = A002859(1) + A002859(4), so a(5) = min(1,4) = 1.
A002859(6) = 8 = 3 + 5 = A002859(2) + A002859(4), so a(6) = min(2,4) = 2.
A002859(7) = 10 = 4 + 6 = A002859(3) + A002859(5), so a(7) = min(3,5) = 3.
(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 := min(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, A049877, A049879.

Sequence in context: A140605 A350064 A351085 * A038203 A255239 A316339

Adjacent sequences: A049875 A049876 A049877 * A049879 A049880 A049881

Keyword

nonn

Author

Clark Kimberling

Extensions

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

More terms from Petros Hadjicostas, Nov 20 2019

Status

approved