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Search: id:A090073
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| A090073 |
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a(n) = least number m such that m-1, m+1 are twin primes, m=a*b, and there are 2^n - 1 choices for (S, D) where S=a+b, D=a-b (a>b>1) and with both S and D primes. |
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+0
3
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OFFSET
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1,1
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COMMENT
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Note that (m-1)^2+S^2=(m+1)^2+D^2.
If k is the number of distinct prime factors of m, then the maximum number of (S, D) values both primes is 2^(k-1)-1. 18, 60, and 1932 are the only terms of the sequence with all (S, D) values both primes. If we consider 1 to be prime (and pi(1)=0), then the first 3 terms are 6, 30, 462
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EXAMPLE
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m=18,(m-1,m+1)=(17,19),{(S,D)}={(11,7)}
m=60,(m-1,m+1)=(59,61),{(S,D)}={(23,17),(19,11),(17,7)}
m=1932 7 (S,D) prime values
m=43890 15 (S,D) prime values....
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CROSSREFS
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Sequence in context: A056448 A056438 A105521 this_sequence A016728 A010006 A044156
Adjacent sequences: A090070 A090071 A090072 this_sequence A090074 A090075 A090076
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KEYWORD
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hard,more,nonn
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AUTHOR
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Robin Garcia (verob99(AT)teleline.es), Jan 21 2004
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