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A120403
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a(1)=3; a(n)=first odd number greater than a(n-1) such that 2*a(n)-1 is prime and a(i)+a(n)-1 is prime for all 1<=i<=n-1.
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0
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3, 9, 15, 45, 225, 639, 1275, 4005, 675405, 2203959, 3075159, 6195234165, 77989711185, 4566262987329
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OFFSET
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1,1
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COMMENTS
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All elements are 3 mod 6. In base 12 the sequence is 3, 9, 13, 39, 169, 453, 8X3, 2399, 286X39, 8X3533, 1043733, where X is 10 and E is eleven.
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LINKS
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FORMULA
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a(1)=3; a(n) = s where s is the first odd number s>a(n-1) such that 2*s-1 is prime and s+a(i)-1 is prime, 1<=i<=n-1.
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EXAMPLE
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a(2)=9 since 9 is the first odd number > a(1)=3 such that 2*9-1=17 is prime and 9+3-1=13 is prime.
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MAPLE
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OP:=[3]: for w to 1 do for k from 0 to 12^8 do n:=6*k+3; p:=2*n-1; Q:=map(z-> z+n-1, OP); if isprime(p) and andmap(isprime, Q) then OP:=[op(OP), n]; print(n); fi od od;
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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