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A225669
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Slowest-growing sequence of odd primes whose reciprocals sum to 1.
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3
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3, 5, 7, 11, 13, 17, 19, 23, 967, 101419, 2000490719, 106298338760698351, 586903266015193517540253132922939, 3494365451928289992209032562272585187947069047023572601254975717
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OFFSET
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1,1
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COMMENTS
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See comments, references, and links in A075442 = slowest-growing sequence of primes whose reciprocals sum to 1.
a(n) = 3, 5, 7, 11, 13, 17, 19, 23, 967, ..., so A225671(2) = 23.
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REFERENCES
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Popular Computing (Calabasas, CA), Problem 175: A Sum of a Different Kind, Vol. 5 (No. 50, May 1977), p. PC50-8.
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LINKS
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EXAMPLE
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Since 1/3 + 1/5 + 1/7 + 1/11 + 1/13 + 1/17 + 1/19 + 1/23 < 1, the first eight odd primes are members. The ninth is not, because adding 1/29 pushes the sum over 1.
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MATHEMATICA
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a[n_] := a[n] = Block[{sm = Sum[1/(a[i]), {i, n - 1}]}, NextPrime[ Max[ a[n - 1], 1/(1 - sm)]]]; a[0] = 2; Array[a, 14]
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CROSSREFS
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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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