OFFSET
1,1
COMMENTS
The sums are the difference of two triangular numbers A000217. The common numbers themselves are A094550. The sums, n > 0, are n = (b-a+1)(a+b)/2 = (b+c)(c-b+1)/2 where b^2 + a - a^2 = c^2 + c - b^2, is solvable in integers for 0 < a < b < c. Since the runs have something in common, they are "friends". The series of sums *without* the common number is A110702. The numbers common to the two runs are A094550.
LINKS
Ron Knott Runsums
T. Verhoeff, Rectangular and Trapezoidal Arrangements, J. Integer Sequences, Vol. 2, 1999, #99.1.6.
EXAMPLE
2 + 3 + 4 = 4 + 5 share the common number 4. The sum of both is 9 and this is the smallest such sum with a common "friend" (4), so a(1)=9.
CROSSREFS
KEYWORD
nonn
AUTHOR
Ron Knott, Aug 04 2005
STATUS
approved