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A248133 Least positive integer m such that m + n divides T(m) + T(n), where T(.) is given by A002426. 6
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 (list; graph; refs; listen; history; text; internal format)
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 * A228524 A116407 A309402

Adjacent sequences:  A248130 A248131 A248132 * A248134 A248135 A248136

KEYWORD

nonn

AUTHOR

Zhi-Wei Sun, Oct 02 2014

STATUS

approved

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Last modified July 13 16:22 EDT 2020. Contains 335688 sequences. (Running on oeis4.)