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A091963
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a(n) is the smallest gcd of two interior numbers on row n of Pascal's triangle ("interior" means that the 1's at the ends of the rows are excluded).
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3
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2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 3, 13, 2, 3, 2, 17, 2, 19, 4, 3, 2, 23, 3, 5, 2, 3, 4, 29, 6, 31, 2, 3, 2, 5, 4, 37, 2, 3, 5, 41, 6, 43, 4, 3, 2, 47, 3, 7, 2, 3, 4, 53, 2, 5, 7, 3, 2, 59, 4, 61, 2, 7, 2, 5, 6, 67, 4, 3, 10, 71, 4, 73, 2, 3, 4, 7, 2, 79, 5, 3, 2, 83, 12, 5, 2, 3, 4, 89, 9, 7, 4, 3, 2, 5, 3
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OFFSET
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2,1
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COMMENTS
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The reference contains a simple proof that there are no 1's in this sequence.
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REFERENCES
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R. K. Guy, Unsolved Problems in Number Theory, Sections B31, B33.
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LINKS
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EXAMPLE
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In row 8, the interior numbers 8, 28, 56 and 70; gcd(8, 28) = 4; gcd(8, 56) = 8; gcd(8, 70) = 2; gcd(28, 56) = 28; gcd(28, 70) = 14; gcd(56, 70) = 14. The smallest of these is 2, so a(8) = 2.
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MAPLE
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seq(min(seq(igcd(n, binomial(n, k)), k=1..floor(n/2))), n=2..100); # Robert Israel, Jun 17 2014
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PROG
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(PARI) a(n) = {v = vector(n\2, i, binomial(n, i)); mgcd = n; for (i=1, #v, for (j=i+1, #v, mgcd = min(gcd(v[i], v[j]), mgcd); ); ); return (mgcd); } \\ Michel Marcus, Jun 16 2013
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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