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A059960
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Smaller term of a pair of twin primes such that prime factors of their average are only 2 and 3.
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18
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5, 11, 17, 71, 107, 191, 431, 1151, 2591, 139967, 472391, 786431, 995327, 57395627, 63700991, 169869311, 4076863487, 10871635967, 2348273369087, 56358560858111, 79164837199871, 84537841287167, 150289495621631
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OFFSET
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1,1
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COMMENTS
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Primes p(k) such that the number of distinct prime divisors of all composite numbers between p(k) and p(k+1) is 2. - Amarnath Murthy, Sep 26 2002
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LINKS
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FORMULA
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Primes p such that p+1 = (2^u)*(3^w)
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EXAMPLE
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a(11)+1 = 2*2*2*3*3*3*3*3*3*3*3*3*3 = 472392.
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MATHEMATICA
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nn=10^15; Sort[Reap[Do[n=2^i 3^j; If[n<=nn && PrimeQ[n-1] && PrimeQ[n+1], Sow[n-1]], {i, Log[2, nn]}, {j, Log[3, nn]}]][[2, 1]]]
Select[Select[Partition[Prime[Range[38*10^5]], 2, 1], #[[2]]-#[[1]]==2&][[All, 1]], FactorInteger[#+1][[All, 1]]=={2, 3}&] (* The program generates the first 15 terms of the sequence. *)
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CROSSREFS
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Apart from initial terms, same as A078883.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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