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A118478
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a(n) is the smallest m such that m(m+1) is divisible by the first n prime numbers.
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1
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1, 2, 5, 14, 209, 714, 714, 62985, 367080, 728364, 64822394, 1306238010, 11182598504, 715041747420, 51913478860880, 454746157008780, 9314160363311804, 261062105979210899, 261062105979210899
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n)*(a(n)+1)/n# = 1, 1, 1, 1, 19, 17, 1, 409, 604, 82, 20951, 229931, 411012, 39080794, 4382914408, ..., . - Robert G. Wilson v May 13 2006.
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LINKS
| Robert Gerbicz (robert.gerbicz(AT)gmail.com), Aug 24 2006, Table of n, a(n) for n = 1..25
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FORMULA
| a(n)=min(k) such that n# | k(k+1), where n#=p_1*p_2*...*p_n is the n-th primorial number. (A002110)
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EXAMPLE
| a(8)=62985 since 62985*62986 = 2*3*5*7*11*13*17*19*409, i.e., it is divisible by the first 8 prime numbers (2,3,..,19).
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MATHEMATICA
| f[n_] := Block[{k = 1, p = Times @@ Prime@Range@n}, While[ !IntegerQ@ Sqrt[4k*p + 1], k++ ]; Floor@ Sqrt[k*p]]; Array[f, 15] (from Robert G. Wilson v (rgwv(at)rgwv.com), May 13 2006)
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PROG
| (PARI) P=primes(25); T=1; for(n=1, 25, T*=P[n]; m=T; for(k=2^(n-1), 2^n-1, u=binary(k); a=1; for(i=1, n, if(u[i], a*=P[i])); b=T/a; w=bezout(a, b); if(w[1]<=0, w[1]+=b); c=a*w[1]-1; m=min(m, c); w[1]=b-w[1]; if(w[1]<=0, w[1]+=b); c=a*w[1]; m=min(m, c)); print1(m, ", ")) - Robert Gerbicz (robert.gerbicz(AT)gmail.com), Aug 24 2006
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CROSSREFS
| Cf. A002110, A059958.
Sequence in context: A102019 A097595 A081483 * A179675 A193314 A146116
Adjacent sequences: A118475 A118476 A118477 * A118479 A118480 A118481
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KEYWORD
| nonn
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AUTHOR
| Giovanni Resta (g.resta(AT)iit.cnr.it), May 05 2006
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EXTENSIONS
| More terms from Robert Gerbicz (robert.gerbicz(AT)gmail.com), Aug 24 2006
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