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 A118478 a(n) is the smallest m such that m*(m+1) is divisible by the first n prime numbers. 4

%I

%S 1,2,5,14,209,714,714,62985,367080,728364,64822394,1306238010,

%T 11182598504,715041747420,51913478860880,454746157008780,

%U 9314160363311804,261062105979210899,261062105979210899,696537082207206753590,54097844397380813592485,286495021083846822067820

%N a(n) is the smallest m such that m*(m+1) is divisible by the first n prime numbers.

%C a(n)*(a(n)+1)/(product of first n primes) = 1, 1, 1, 1, 19, 17, 1, 409, 604, 82, 20951, 229931, 411012, 39080794, 4382914408, ... - _Robert G. Wilson v_, May 13 2006 [This is now A215021. - _N. J. A. Sloane_, Aug 02 2012]

%H Jinyuan Wang, <a href="/A118478/b118478.txt">Table of n, a(n) for n = 1..30</a> (terms 1..25 from Robert Gerbicz)

%F a(n) = Min_{m | m*(m+1) is divisible by A002110(n)}.

%e 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).

%t f[n_] := Block[{k = 1, p = Times @@ Prime@Range@n}, While[ !IntegerQ@ Sqrt[4k*p + 1], k++ ]; Floor@ Sqrt[k*p]]; Array[f, 15] (* _Robert G. Wilson v_, May 13 2006 *)

%o (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_, Aug 24 2006

%o import Data.List (elemIndex); import Data.Maybe (fromJust)

%o a118478 n = (+ 1) . fromJust \$ elemIndex 0 \$

%o map (flip mod (a002110 n)) \$ tail a002378_list

%o -- _Reinhard Zumkeller_, Jun 14 2015

%Y Cf. A002110, A002378, A193314, A215021, A053670, A059958.

%K nonn

%O 1,2

%A _Giovanni Resta_, May 05 2006

%E More terms from _Robert Gerbicz_, Aug 24 2006

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Last modified May 6 15:28 EDT 2021. Contains 343586 sequences. (Running on oeis4.)