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A078777
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a(n) = the least positive integer k such that binomial(2k,k) + k + n is prime, if such k exists; = 0, otherwise.
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0
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1, 0, 1, 2, 1, 2, 3, 6, 1, 2, 1, 2, 5, 120, 1, 2, 1, 6, 3, 58, 1, 2, 7, 2, 3, 12, 1, 4, 1, 2, 3, 12, 9, 2, 1, 2, 3, 6, 1, 2, 1, 6, 19, 16, 1, 2, 13, 6, 3, 12, 1, 2, 7, 2, 5, 16, 1, 4, 1, 2, 3, 6, 15, 2, 1, 2, 3, 6, 1, 14, 1, 2, 7, 16, 3, 2, 1, 4, 3, 6, 1
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OFFSET
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0,4
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COMMENTS
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The value a(1) = 0 is conjectural. There is no k < 8.5 x 10^3 such that binomial(2k,k)+k+1 is prime.
There is no k < 10^8 making binomial(2k,k)+k+1 prime. - Charles R Greathouse IV, May 19 2013
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LINKS
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Table of n, a(n) for n=0..80.
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EXAMPLE
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k=2 is the least positive integer such that binomial(2k,k) + k + 3 is prime. Hence a(2) = 3.
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PROG
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(PARI) a(n) = {k = 1; while(! isprime(binomial(2*k, k) + k + n), k++; if (k % 1000 == 0, print(k)); ); return (k); } \\ Michel Marcus, May 19 2013
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CROSSREFS
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Sequence in context: A204994 A132405 A057192 * A135938 A079210 A070861
Adjacent sequences: A078774 A078775 A078776 * A078778 A078779 A078780
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KEYWORD
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nonn,changed
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AUTHOR
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Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Jan 09 2003
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EXTENSIONS
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a(0) = 1 prepended to sequence to match offset by Michel Marcus, May 19 2013
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STATUS
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approved
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