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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.
2
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
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
Sequence in context: A328493 A225583 A180932 * A139580 A156897 A094841
KEYWORD
hard,more,nonn
AUTHOR
EXTENSIONS
a(8) from Robin Visser, Sep 08 2023
STATUS
approved