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A177983
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a(1)=3. Otherwise the average of the least prime divisors of 2n-1 and 2n+3.
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2
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3, 5, 4, 9, 8, 7, 15, 11, 10, 21, 4, 13, 17, 17, 16, 18, 20, 4, 39, 23, 22, 45, 5, 25, 30, 4, 28, 32, 32, 31, 33, 35, 4, 69, 38, 37, 40, 41, 5, 81, 4, 43, 47, 5, 46, 6, 50, 4, 99, 53, 52, 105, 56, 55, 111, 4, 58, 6, 7, 5, 8, 65, 4, 129, 5, 67, 72, 71, 70, 75, 4, 7, 77, 77, 76, 78, 80, 4, 82, 83
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OFFSET
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1,1
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COMMENTS
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Lim inf (n->infinity) (a(n)/n)=0.
If there exist infinitely many cousin primes (A023200), then lim sup (n->infinity) (a(n)/ n)=2.
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LINKS
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FORMULA
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MAPLE
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MATHEMATICA
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Table[Mean[{FactorInteger[2n-1][[1, 1]], FactorInteger[2n+3][[1, 1]]}], {n, 80}] (* Harvey P. Dale, Nov 08 2022 *)
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PROG
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(PARI) a(n) = if (n==1, 3, (factor(2*n-1)[1, 1] + factor(2*n+3)[1, 1])/2); \\ Michel Marcus, Feb 08 2016
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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