A248133 Least positive integer m such that m + n divides T(m) + T(n), where T(.) is given by A002426.

1, 3, 1, 1, 7, 2, 2, 2, 1, 1, 7, 4, 37, 145, 35, 1, 25, 16, 5, 16, 1, 1, 18, 19, 3, 11, 41, 1, 7, 2, 48, 415, 1, 2, 15, 7, 13, 34, 97, 1, 27, 18, 56, 22, 1, 1, 5, 26, 22, 36, 18, 1, 117, 52, 376, 11, 1, 1, 23, 26

Offset

1,2

Comments

Conjecture: a(n) exists for any n > 0. Moreover, a(n) <= n^2 - n + 1 except for n = 274.

Note that a(274) = 188847 > 2*274^2.

Links

Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

Example

a(5) = 7 since 5 + 7 divides T(5) + T(7) = 51 + 393 = 444 = 12*37.
a(2539) = 643425 since 2539 + 643425 = 645964 divides T(2539) + T(643425).

Mathematica

T[n_]:=Sum[Binomial[n, 2k]Binomial[2k, k], {k, 0, n/2}]
Do[m=1; Label[aa]; If[Mod[T[m]+T[n], m+n]==0, Print[n, " ", m]; Goto[bb]]; m=m+1; Goto[aa]; Label[bb]; Continue, {n, 1, 60}]

Crossrefs

Cf. A002426, A247824, A247937, A247940, A248124, A248125, A248136, A248137, A248139, A248142.

Sequence in context: A228035 A332538 A071812 * A177992 A346906 A228524

Adjacent sequences: A248130 A248131 A248132 * A248134 A248135 A248136

Keyword

nonn

Author

Zhi-Wei Sun, Oct 02 2014

Status

approved