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 A276781 a(n) = minimal b such that the numbers binomial(n,k) for b <= k <= n-b have a common divisor greater than 1. 2
 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 3, 1, 1, 2, 1, 2, 3, 4, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 3, 4, 5, 1, 2, 3, 4, 1, 2, 1, 2, 3, 4, 1, 2, 1, 2, 3, 4, 1, 2, 3, 4, 5, 6, 1, 2, 1, 2, 3, 1, 2, 3, 1, 2, 3, 4, 1, 2, 1, 2, 3, 4, 5, 6, 1, 2, 1, 2, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 1, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,5 COMMENTS The definition in the video has "b < k < n-b" rather than "b <= k <= n-b", but that appears to be a typographical error. LINKS R. J. Mathar and Chai Wah Wu, Table of n, a(n) for n = 2..10000 (terms for n = 2..1685 from R. J. Mathar). Christophe Soulé, Le triangle de Pascal et ses propriétés, Lecture, Soc. Math. de France, Feb 13 2008. EXAMPLE Row 6 of Pascal's triangle is 1,6,15,20,15,6,1 and [15,20,15] have a common divisor of 5. Since 15 = binomial(6,2), a(6)=2. MAPLE mygcd:=proc(lis) local i, g, m; m:=nops(lis); g:=lis[1]; for i from 2 to m do g:=gcd(g, lis[i]); od: g; end; f:=proc(n) local b, lis; global mygcd; for b from floor(n/2) by -1 to 1 do lis:=[seq(binomial(n, i), i=b..n-b)]; if mygcd(lis)=1 then break; fi; od: b+1; end; [seq(f(n), n=2..120)]; MATHEMATICA Table[b = 1; While[GCD @@ Map[Binomial[n, #] &, Range[b, n - b]] == 1, b++]; b, {n, 92}] (* Michael De Vlieger, Oct 03 2016 *) CROSSREFS Cf. A007318, A276782 (positions of records). Sequence in context: A206824 A293810 A324369 * A303759 A082068 A300360 Adjacent sequences:  A276778 A276779 A276780 * A276782 A276783 A276784 KEYWORD nonn AUTHOR N. J. A. Sloane, Sep 29 2016, following a suggestion from Eric Desbiaux. STATUS approved

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Last modified May 26 04:46 EDT 2019. Contains 323579 sequences. (Running on oeis4.)