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A003458
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Erdos-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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1
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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REFERENCES
| R. Scheidler and H. C. Williams, A method of tabulating the number-theoretic function g(k), Math. Comp., 59 (1992), 251-257.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..200 (from H. C. Williams)
E. F. Ecklund, Jr. et al., A new function associated with the prime factors of C(n,k), Math. Comp., 28 (1974), 647-649.
R. F. Lukes; R. Scheidler; H. C. Williams, Further Tabulation of the Erdos-Selfridge Function, Math. Comput. 66 (1997) 1709-1717.
R. Scheidler, H. C. Williams, A method for tabulating the number-theoretic function g(k), Math. Comp. 59 (199) (1992) 251-257
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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MAPLE
| A003458 := proc(n) local m, lpfr ; for m from n+2 do lpfr := numtheory[factorset](binomial(m, n)) ; if min(lpfr) > n then return m; end if; end do: end proc: # R. J. Mathar, Mar 28 2011
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MATHEMATICA
| 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}]
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PROG
| (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 (from R. Stephan)
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CROSSREFS
| Sequence in context: A129023 A188883 A152083 * A133339 A112267 A068985
Adjacent sequences: A003455 A003456 A003457 * A003459 A003460 A003461
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KEYWORD
| easy,nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
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EXTENSIONS
| Extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 01 2002
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