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A119494
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a(n) = smallest prime number p_k such that 1/p_n + 1/p_{n+1} + ... + 1/p_k > 1.
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2
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5, 29, 109, 347, 857, 1627, 2999, 4931, 7759, 11677, 16111, 22229, 29269, 37717, 48527, 61057, 75503, 91463, 110567, 131671, 155509, 183587, 214189, 248597, 286073, 325889, 369983, 419459, 473659, 534043, 600631, 667547, 739549, 816779, 901007, 988661
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OFFSET
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1,1
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COMMENTS
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REFERENCES
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J.-M. De Koninck, Those Fascinating Numbers, Amer. Math. Soc., 2009, page 76, entry 347 and page 108, entry 857.
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LINKS
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FORMULA
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a(n) is approximately prime(n)^e.
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EXAMPLE
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a(2) = 29 because 1/3 + 1/5 + 1/7 + 1/11 + 1/13 + 1/17 + 1/19 + 1/23 + 1/29 = 1.0334... > 1 and 1/3 + 1/5 + 1/7 + 1/11 + 1/13 + 1/17 + 1/19 + 1/23 = 0.9989... < 1.
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MATHEMATICA
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f[0]={0, 0}; f[n_] := f[n] = Module[{f1=f[n-1]}, p=f1[[1]]; s=f1[[2]]-If[n>1, 1/Prime[n-1], 0]; While[s<1, p=NextPrime[p]; s+=1/p]; {p, s}]; f[#][[1]] & /@ Range[30] (* Amiram Eldar, Dec 24 2018 *)
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PROG
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(PARI) a(n)=my(s=0.); forprime(p=prime(n), default(primelimit), s+=1/p; if(s>1, return(p)))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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