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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.)