A242170 Least prime divisor of T(n) which does not divide any T(k) with k < n, or 1 if such a primitive prime divisor of T(n) does not exist, where T(n) is the n-th central trinomial coefficient given by A002426.

1, 3, 7, 19, 17, 47, 131, 41, 43, 1279, 503, 113, 2917, 569, 198623, 14083, 26693, 201611, 42998951, 41931041, 52635749, 1296973, 169097, 1451, 1304394227, 107, 233, 173, 2062225210273, 719, 191, 31551555041, 6301, 563, 3769, 967, 9539, 5073466546857451, 4542977, 9739

Offset

1,2

Comments

Conjecture: (i) a(n) > 1 for all n > 1.

(ii) For any integer n > 3, the n-th Motzkin number M(n) given by A001006 has a prime divisor which does not divide any M(k) with k < n.

Links

Zhi-Wei Sun, Table of n, a(n) for n = 1..168

Example

a(11) = 503 since T(11) = 3*17*503 with the prime divisor 503 dividing none of T(1),...,T(10), but 3 divides T(2) = 3 and 17 divides T(5) = 51.

Mathematica

T[n_]:=Sum[Binomial[n, 2k]*Binomial[2k, k], {k, 0, n/2}]
f[n_]:=FactorInteger[T[n]]
p[n_]:=Table[Part[Part[f[n], k], 1], {k, 1, Length[f[n]]}]
Do[If[T[n]<2, Goto[cc]]; Do[Do[If[Mod[T[i], Part[p[n], k]]==0, Goto[aa]], {i, 1, n-1}];
Print[n, " ", Part[p[n], k]]; Goto[bb]; Label[aa]; Continue, {k, 1, Length[p[n]]}];
Label[cc]; Print[n, " ", 1]; Label[bb]; Continue, {n, 1, 40}]

Crossrefs

Cf. A000040, A001006, A002426, A242169, A242171, A242173.

Sequence in context: A083439 A151858 A365139 * A032675 A089749 A032667

Adjacent sequences: A242167 A242168 A242169 * A242171 A242172 A242173

Keyword

nonn

Author

Zhi-Wei Sun, May 05 2014

Status

approved