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

1,1

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.

Links

Table of n, a(n) for n=1..53.

Ron Knott Runsums

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

Example

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)).

Crossrefs

Cf. A001227, A094550, A110701, A110703.

Sequence in context: A274535 A027184 A328249 * A141394 A127256 A136139

Adjacent sequences: A110699 A110700 A110701 * A110703 A110704 A110705

Keyword

nonn

Author

Ron Knott, Aug 04 2005

Status

approved