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 A267825 Index of largest primorial factor of binomial(2n,n). 1
 0, 1, 2, 1, 1, 2, 2, 2, 3, 1, 1, 2, 1, 1, 3, 3, 3, 3, 5, 5, 6, 3, 3, 3, 3, 2, 2, 1, 1, 5, 1, 1, 2, 4, 4, 2, 1, 1, 4, 1, 1, 5, 5, 5, 4, 4, 4, 4, 4, 3, 2, 2, 2, 5, 5, 2, 2, 2, 3, 3, 2, 2, 2, 3, 3, 3, 3, 5, 5, 5, 3, 3, 3, 3, 6, 6, 6, 7, 5, 5, 5, 1, 1, 5, 1, 1, 6, 6, 6, 6, 1, 1, 6, 1, 1, 7, 7, 7, 3, 3, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS For n > 0, binomial(2n,n) is even, so a(n) >= 1. Is a(n) unbounded? (The largest value for n <= 100000 is a(45416) = 43.) From Robert Israel, Jan 28 2016: (Start) a(n) = A000720(p)-1 where p is the least prime that does not divide A000984(n). Equivalently, p is the least prime such that the base-p representation of n has all digits < p/2. a(primorial(k)-1) >= k. In particular the sequence is unbounded. (End) LINKS Table of n, a(n) for n=0..100. Wikipedia, Lucas' theorem FORMULA a(A267823(n)) >= n. min{k : a(k) >= n} = A267823(n). EXAMPLE Binomial(16,8) = 12870 is divisible by primorial(3) = 2*3*5 = 30, but not by prime(4) = 7, so a(8) = 3. MATHEMATICA PrimorialFactor[n_] := (k = 0; While[Mod[n, Prime[k + 1]] == 0, k++]; k); Table[PrimorialFactor[Binomial[2 n, n]], {n, 0, 100}] PROG (PARI) pf(n) = {my(k = 0); while (n % prime(k+1) == 0, k++); k; } a(n) = pf(binomial(2*n, n)); \\ adapted from Mathematica; Michel Marcus, Jan 29 2016 CROSSREFS Cf. A000720, A000984, A002110, A226078, A267823. Sequence in context: A090822 A091975 A091976 * A151902 A094839 A341771 Adjacent sequences: A267822 A267823 A267824 * A267826 A267827 A267828 KEYWORD nonn AUTHOR Jonathan Sondow, Jan 27 2016 STATUS approved

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Last modified April 13 02:05 EDT 2024. Contains 371639 sequences. (Running on oeis4.)