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.
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
Examples
a(4)=15 because k=2 and prime factors are 3 and 5; 15 is odd and n-2=13, prime.
Programs
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Mathematica
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 *)
Extensions
Edited, corrected and extended by Farideh Firoozbakht, Aug 13 2009
Comments