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Search: id:A110702
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| A110702 |
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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. |
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+0
3
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| 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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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.
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REFERENCES
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T. Verhoeff, Rectangular and Trapezoidal Arrangements, J. Integer Sequences, Vol. 2, 1999, #99.1.6.
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LINKS
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R. Knott Runsums
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EXAMPLE
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1+2+3+4+5 and 7+8 have a gap between then of (6). The sum of both is 15 so 15 is in the ordered series (as a(2))
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CROSSREFS
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Cf. A001227, A094550, A110701, A110703.
Adjacent sequences: A110699 A110700 A110701 this_sequence A110703 A110704 A110705
Sequence in context: A032472 A045176 A027184 this_sequence A141394 A127256 A136139
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KEYWORD
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nonn
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AUTHOR
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Ron Knott (enquiry(AT)ronknott.com), Aug 04 2005
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