A110702 Numbers S with two runsums (sum of positive integer runs) where the 2 runs are separated by a single number gap (b), i.e., S = a + (a+1) + ... + (b-1) = (b+1) + ... + c with a < b-1, b < c.

5, 15, 21, 33, 54, 54, 85, 90, 100, 117, 110, 135, 153, 161, 204, 195, 252, 261, 315, 308, 315, 315, 351, 385, 405, 418, 414, 450, 455, 476, 510, 533, 595, 609, 637, 650, 705, 693, 684, 777, 792, 870, 884, 931, 986, 999, 1071, 1105, 1121, 1110, 1125, 1210, 1230

Offset: 1

Author

Ron Knott, Aug 04 2005

Keywords

• nonn

Comments

The sums are the difference of two triangular numbers A000217. The sum series where the missing number is included is A110701. The numbers in the gap between the two runs are A094550.

Examples

			1+2+3+4+5 and 7+8 have a gap between them of (6). The sum of both is 15 so 15 is in the ordered series (as a(2)).
		

Links

• Ron Knott Runsums
• T. Verhoeff, Rectangular and Trapezoidal Arrangements, J. Integer Sequences, Vol. 2, 1999, #99.1.6.

Crossrefs

Cf. A001227, A094550, A110701, A110703.