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A136358
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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.
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6
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4, 6, 9, 15, 30, 105, 420, 2310, 3465, 15015, 180180, 765765, 4084080, 106696590, 247342095, 892371480, 3011753745, 9704539845, 100280245065, 103515091680, 4412330782860, 29682952539240, 634473110526255, 22514519501013540
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OFFSET
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1,1
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COMMENTS
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
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PROG
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(UBASIC)
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
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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