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A003458
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Erdős-Selfridge function: a(n) is the least number m > n+1 such that the least prime factor of binomial(m, n) is > n.
(Formerly M2515)
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3
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3, 6, 7, 7, 23, 62, 143, 44, 159, 46, 47, 174, 2239, 239, 719, 241, 5849, 2098, 2099, 43196, 14871, 19574, 35423, 193049, 2105, 36287, 1119, 284, 240479, 58782, 341087, 371942, 6459, 69614, 37619, 152188, 152189, 487343, 767919, 85741, 3017321
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OFFSET
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1,1
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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MAPLE
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local m;
for m from n+2 do
if A020639( binomial(m, n)) > n then
return m ;
end if;
end do:
end proc:
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MATHEMATICA
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f[n_] := Block[{k = n + 2, p = Table[Prime[i], {i, 1, PrimePi[n]}]}, While[ First[ Sort[ Mod[ Binomial[k, n], p]]] == 0, k++ ]; k]; Table[ f[n], {n, 1, 40}]
esf[n_]:=Module[{m=n+2}, While[FactorInteger[Binomial[m, n]][[1, 1]]<=n, m++]; m]; Array[esf, 50] (* Harvey P. Dale, Nov 03 2013 *)
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PROG
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(PARI) a(n) = local(m, i, f); m=0; i=n+1; while(m<=n, i=i+1; m=factor(binomial(i, n))[1, 1]); i /* Ralf Stephan */
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CROSSREFS
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KEYWORD
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easy,nonn,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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