This site is supported by donations to The OEIS Foundation.



Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A140601 Values of m such that binomial(m, a) + binomial(m, b) divides binomial(m, a + b) for some distinct nonnegative integers a and b with a + b <= m. 2
19, 34, 41, 89, 104, 359, 398, 495, 527, 1845, 2309, 2729, 3539, 4619, 8644, 12923, 14135, 15774 (list; graph; refs; listen; history; text; internal format)



This sequence was first suggested by Stefan Steinerberger, who conjectures that there are infinitely many terms.

Next term (if it exists) is greater than 25325. - Max Alekseyev

For every fixed pair of integers a,b, there exists only a finite number of suitable values of m. - Max Alekseyev

For all known entries (up to a(18)), there is exactly one pair (a,b) which satisfies the required conditions. In every case b-a is either 1 or 2. See sequence A140602 for values with b-a = 1 and A140603 for b-a = 2. Related open questions: (1) Must the pair (a,b) for a given a(n) be unique? (2) Does every solution have b-a <= 2?


Table of n, a(n) for n=1..18.


C(19,3) + C(19,5) divides C(19,8)

C(34,6) + C(34,7) divides C(34,13)

C(41,5) + C(41,7) divides C(41,12)

C(89,7) + C(89,8) divides C(89,15)

C(104,3) + C(104,4) divides C(104,7)

C(359,5) + C(359,6) divides C(359,11)

C(398,20) + C(398,21) divides C(398,41)

C(495,12) + C(495,14) divides C(495,26)

C(527,7) + C(527,9) divides C(527,16)

C(1845,15) + C(1845,17) divides C(1845,32)

C(2309,5) + C(2309,6) divides C(2309,11)

C(2729,19) + C(2729,20) divides C(2729,39)

C(3539,35) + C(3539,36) divides C(3539,71)

C(4619,11) + C(4619,12) divides C(4619,23)

C(8644,18) + C(8644,19) divides C(8644,37)

C(12923,34) + C(12923,36) divides C(12923,70)

C(14135,30) + C(14135,31) divides C(14135,61)

C(15774,24) + C(15774,26) divides C(15774,50)


Cf. A140602, A140603.

Sequence in context: A146438 A146571 A235869 * A031206 A214231 A242847

Adjacent sequences:  A140598 A140599 A140600 * A140602 A140603 A140604




Andrew V. Sutherland, May 18 2008


Edited by Max Alekseyev, Jun 16 2010



Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified November 19 07:16 EST 2017. Contains 294916 sequences.