A049879 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).

1, 2, 3, 2, 2, 3, 4, 6, 4, 7, 9, 7, 10, 12, 12, 14, 12, 15, 17, 17, 19, 17, 20, 22, 5, 26, 25, 19, 27, 16, 29, 13, 31, 33, 33, 31, 8, 6, 37, 3, 39, 19, 40, 42, 42, 44, 4, 46, 6, 48, 48, 8, 50, 11, 53, 53, 55, 53, 16, 58, 58, 17, 60, 19, 63, 23, 65, 25, 67, 11, 70, 70, 68, 33, 58, 35, 74

Offset

3,2

Links

Table of n, a(n) for n=3..79.

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) = |1-2| = 1.
A002859(4) = 5 = 1 + 4 = A002859(1) + A002859(3), so a(4) = |1-3| = 2.
A002859(5) = 6 = 1 + 5 = A002859(1) + A002859(4), so a(5) = |1-4| = 3.
A002859(6) = 8 = 3 + 5 = A002859(2) + A002859(4), so a(6) = |2-4| = 2.
A002859(7) = 10 = 4 + 6 = A002859(3) + A002859(5), so a(7) = |3-5| = 2.
(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 := abs(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, A049878.

Sequence in context: A358639 A358640 A096258 * A053812 A177865 A307835

Adjacent sequences: A049876 A049877 A049878 * A049880 A049881 A049882

Keyword

nonn

Author

Clark Kimberling

Extensions

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

Status

approved