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A003458 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)
1
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; text; internal format)
OFFSET

1,1

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).

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, Erdős-Selfridge function.

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

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}]

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 *)

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 /* Ralf Stephan */

CROSSREFS

Sequence in context: A251532 A251533 A295849 * A133339 A112267 A068985

Adjacent sequences:  A003455 A003456 A003457 * A003459 A003460 A003461

KEYWORD

easy,nonn,nice

AUTHOR

N. J. A. Sloane, Simon Plouffe

EXTENSIONS

Extended by Robert G. Wilson v, Dec 01 2002

STATUS

approved

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Last modified August 20 08:27 EDT 2019. Contains 326143 sequences. (Running on oeis4.)