A140603 Values of m for which C(m,k) + C(m,k+2) divides C(m,2k+2) for some nonnegative integer k with 2k+2 <= m.

19, 41, 495, 527, 1845, 12923, 15774, 36098

Offset

1,1

Comments

See A140601, which is the main entry for this sequence.

a(9) (if it exists) is greater than 170000. - Robin Visser, Sep 08 2023

Links

Table of n, a(n) for n=1..8.

Example

a(1) = 19 because C(19,3) + C(19,5) = 969 + 11628 = 12597 divides C(19,8) = 75582, and 19 is the smallest nonnegative integer for which the required condition holds.
From Robin Visser, Sep 09 2023: (Start)
Terms a(2) to a(8) are given by the following divisibility relations:
  C(41,5) + C(41,7) divides C(41,12),
  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(12923,34) + C(12923,36) divides C(12923,70),
  C(15774,24) + C(15774,26) divides C(15774,50),
  C(36098,34) + C(36098,36) divides C(36098,70). (End)

Prog

(Sage)
for m in range(2, 100000):
    for a in range(0, m//2):
        if (binomial(m, 2*a+2)%(binomial(m, a)+binomial(m, a+2)) == 0):
            print(m); break  # Robin Visser, Sep 08 2023

Crossrefs

Cf. A140601, A140602.

Sequence in context: A328493 A225583 A180932 * A139580 A156897 A094841

Adjacent sequences: A140600 A140601 A140602 * A140604 A140605 A140606

Keyword

hard,more,nonn

Author

Andrew V. Sutherland, May 18 2008

Extensions

a(8) from Robin Visser, Sep 08 2023

Status

approved