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 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. 11
 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 (list; graph; refs; listen; history; text; internal format)
 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: A075609 A083439 A151858 * A032675 A089749 A032667 Adjacent sequences:  A242167 A242168 A242169 * A242171 A242172 A242173 KEYWORD nonn AUTHOR Zhi-Wei Sun, May 05 2014 STATUS approved

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Last modified July 26 09:29 EDT 2021. Contains 346294 sequences. (Running on oeis4.)