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A318171
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Least prime p such that Sum_{q prime <= p} q is divisible by the first n primes.
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0
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2, 269, 269, 3823, 8539, 729551, 1416329, 23592593, 1478674861, 20458458289, 7558026467353, 201008815538749
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OFFSET
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1,1
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COMMENTS
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a(1)-a(9) are taken from De Koninck's book.
The sequence of indices of these primes is 1, 57, 57, 531, 1065, 58751, 108243, 1483151, 73716417, 901526695, 264119914199, 6301058125383.
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REFERENCES
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Jean-Marie De Koninck, Those Fascinating Numbers, Amer. Math. Soc., 2009, p. 66.
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LINKS
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EXAMPLE
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2 + 3 + ... + 269 = 2 * 3 * 1145
2 + 3 + ... + 269 = 2 * 3 * 5 * 229
2 + 3 + ... + 3823 = 2 * 3 * 5 * 7 * 4473
2 + 3 + ... + 8539 = 2 * 3 * ... * 11 * 1826
2 + 3 + ... + 729551 = 2 * 3 * ... * 13 * 682263
2 + 3 + ... + 1416329 = 2 * 3 * ... * 17 * 143884
2 + 3 + ... + 23592593 = 2 * 3 * ... * 19 * 1742804
2 + 3 + ... + 1478674861 = 2 * 3 * ... * 23 * 237859969
2 + 3 + ... + 20458458289 = 2 * 3 * ... * 29 * 1392427664
2 + 3 + ... + 7558026467353 = 2 * 3 * ... * 31 * 4886311486119
2 + 3 + ... + 201008815538749 = 2 * 3 * ... * 37 * 83956482342243
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MATHEMATICA
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c=0; pr=2; p=2; s=2; q=2; While[c<6, While[!Divisible[s, pr], q = NextPrime[q]; s+=q]; Print[ q]; c++; p = NextPrime[p]; pr*=p]
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PROG
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(PARI) my(c=0, pr=2, p=2, s=2, q=2); while(c<6, while(s%pr!=0, q = nextprime(q+1); s+=q); print1(q, ", "); c++; p = nextprime(p+1); pr*=p)
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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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