|
%I #16 Sep 10 2023 09:08:06
%S 19,41,495,527,1845,12923,15774,36098
%N 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.
%C See A140601, which is the main entry for this sequence.
%C a(9) (if it exists) is greater than 170000. - _Robin Visser_, Sep 08 2023
%e 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.
%e From _Robin Visser_, Sep 09 2023: (Start)
%e Terms a(2) to a(8) are given by the following divisibility relations:
%e C(41,5) + C(41,7) divides C(41,12),
%e C(495,12) + C(495,14) divides C(495,26),
%e C(527,7) + C(527,9) divides C(527,16),
%e C(1845,15) + C(1845,17) divides C(1845,32),
%e C(12923,34) + C(12923,36) divides C(12923,70),
%e C(15774,24) + C(15774,26) divides C(15774,50),
%e C(36098,34) + C(36098,36) divides C(36098,70). (End)
%o (Sage)
%o for m in range(2, 100000):
%o for a in range(0, m//2):
%o if (binomial(m,2*a+2)%(binomial(m,a)+binomial(m,a+2)) == 0):
%o print(m); break # _Robin Visser_, Sep 08 2023
%Y Cf. A140601, A140602.
%K hard,more,nonn
%O 1,1
%A _Andrew V. Sutherland_, May 18 2008
%E a(8) from _Robin Visser_, Sep 08 2023
|
