A136358 Increasing sequence obtained by union of two sequences {b(n)} and {c(n)}, where b(n) is the smallest odd composite number m such that both m-2 and m+2 are prime and the set of distinct prime factors of m consists of the first n odd primes and c(n) is the smallest composite number m such that both m-1 and m+1 are primes and the set of the distinct prime factors of m consists of the first n primes.
4, 6, 9, 15, 30, 105, 420, 2310, 3465, 15015, 180180, 765765, 4084080, 106696590, 247342095, 892371480, 3011753745, 9704539845, 100280245065, 103515091680, 4412330782860, 29682952539240, 634473110526255, 22514519501013540
Offset: 1
Examples
a(1)=4 is preceded by 3 and followed by 5, both primes; a(3)=9, preceded by 7 and followed by 11, both primes.
Programs
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Mathematica
b[n_]:=(d=Product[Prime[k],{k,n}]; For[m=1,!(!PrimeQ[d*m]&&PrimeQ[d*m-1] &&PrimeQ[d*m+1]&&Length[FactorInteger[c*m]]==n),m++ ]; d*m); c[n_]:=(d=Product [Prime[k],{k,2,n+1}]; For[m=1,!(!PrimeQ[d*(2*m-1)]&&PrimeQ[d(2m-1)-2]&&PrimeQ [d(2m-1)+2]&&Length[FactorInteger[d(2m-1)]]==n),m++ ]; d(2m-1)); Take[Union[Table [b[k],{k,24}],Table[c[k],{k,24}]],24] (* Farideh Firoozbakht, Aug 13 2009 *) -
UBASIC
10 'A136358, Enoch Haga, Jun 19 2009' 11 'compute and combine input 2 or 3 separately; begin with 4 and 9 20 input "prime, 2 or 3";A 30 if A=2 or A=3 then B=nxtprm(A) 40 print A;B;:R=A*B:print R;:stop 50 if even(R)=1 then if R-1=prmdiv(R-1) and R+1=prmdiv(R+1) then print "*" 60 if even(R)=0 then if R-2=prmdiv(R-2) and R+2=prmdiv(R+2) then print "+" 61 print R:stop 70 B=nxtprm(B):R=B*R 90 print B;R:stop 100 goto 50 - Enoch Haga, Jul 11 2009
Extensions
Edited, corrected and extended by Farideh Firoozbakht, Aug 13 2009
Comments