A136354
a(n) is the smallest odd composite number m such that m+2 is prime and the set of distinct prime factors of m consists of the first n odd primes.
Original entry on oeis.org
9, 15, 105, 3465, 15015, 765765, 33948915, 334639305, 3234846615, 100280245065, 3710369067405, 1369126185872445, 32706903329175075, 307444891294245705, 211829530101735290745, 961380175077106319535, 762374478836145311391255
Offset: 1
a(1)=9 because k=1 with prime factor 3 and 9+2=11, prime
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a[n_]:=(c=Product[Prime[k],{k,2,n+1}]; For[m=1,!(!PrimeQ[c(2m-1)]&&PrimeQ[c(2m-1)+2]&&Length[FactorInteger[c(2m-1)]]==n),m++ ]; c(2m-1)); Table[a[n],{n,17}] (* Farideh Firoozbakht, Aug 12 2009 *)
A136353
First odd composite N divisible by precisely the first n odd primes with N-2 prime.
Original entry on oeis.org
9, 15, 105, 1155, 15015, 255255, 4849845, 111546435, 9704539845, 100280245065, 18551845337025, 152125131763605, 98120709987525225, 7071232499767651215, 16294579238595022365, 33648306127698721183725, 527797716117331369424715
Offset: 1
The first odd prime is 3, 3*3-2 = 7 is prime so a(1) = 9.
The product of the first two odd primes is 15, and 15-2 is prime, so a(2) = 15.
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a[n_]:=(c=Product[Prime[k],{k,2,n+1}];For[m=1,!(!PrimeQ[c (2m-1)]&&PrimeQ[c(2m-1)-2]&&Length[FactorInteger[c(2m-1)]]==n),m++ ];c(2m-1));Table[a[n],{n,20}] (* Enoch Haga, Jul 02 2009 *)
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sm(n,x)=forprime(p=2,x, n/=p^valuation(n,p)); n==1
a(n)=my(m=factorback(primes(n+1)[2..n+1]),k,p=prime(n+1)); while(!isprime(k++*m-2) && sm(k,p),); k*m \\ Charles R Greathouse IV, Sep 14 2015
A136356
Increasing sequence obtained by union of two sequences A136353 and {b(n)}, where b(n) is the smallest composite number m such that m-1 is prime and the set of distinct prime factors of m consists of the first n primes.
Original entry on oeis.org
4, 6, 9, 15, 30, 105, 420, 1155, 2310, 15015, 30030, 255255, 1021020, 4849845, 19399380, 111546435, 669278610, 9704539845, 38818159380, 100280245065, 601681470390, 14841476269620, 18551845337025, 152125131763605
Offset: 1
a(4)=15 because k=2 and prime factors are 3 and 5; 15 is odd and n-2=13, prime.
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a[n_]:=(c=Product[Prime[k],{k,n}]; For[m=1,!(!PrimeQ[c*m]&&PrimeQ[c*m-1]&&Length[FactorInteger[c*m]]==n),m++ ]; c*m);
b[n_]:=(c=Product[Prime[k],{k,2,n+1}]; For[m=1,!(!PrimeQ[c(2m-1)]&&PrimeQ[c(2m-1)-2]&&Length[FactorInteger[c(2*m-1)]]==n),m++ ]; c(2m-1));
Take[Union[Table[a[k],{k,24}],Table[b[k],{k,24}]],24] (* Farideh Firoozbakht, Aug 13 2009 *)
Showing 1-3 of 3 results.
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