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Search: id:A060380
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| A060380 |
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Let f(m) = smallest prime that divides k^2 + k + m for k = 0,1,2,...; sequence gives smallest m >= 2 such that f(m) is the n-th prime, or -1 if no such m exists. |
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5
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| 2, 3, 5, 47, 11, 221, 17, 1217, 941, 2747, 8081, 9281, 41, 55661, 19421, 333491, 1262201, 601037, 5237651, 9063641, 12899891, 26149427, 24073871, 28537121, 352031501, 398878547, 160834691, 67374467, 146452961, 24169417397
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Chris Nash (see the Prime Puzzles link) has shown that such an m always exists.
For n>2, least odd number d such that the Legedre symbol (1-4d/prime(k)) = -1 for k = 2,...,n, but not for n+1. See A060392. - T. D. Noe (noe(AT)sspectra.com), Apr 19 2004
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REFERENCES
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Fung and Williams, Quadratic polynomials with high density of primes, Mathematics of Computation, Vol. 55, 1990.
R. F. Lukes, C. D. Patterson and H. C. Williams, Numerical sieving devices: their history and some applications. Nieuw Arch. Wisk. (4) 13 (1995), no. 1, 113-139. Math. Rev. 96m:11082
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LINKS
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C. Rivera, www.primepuzzles.net, Conjecture 17
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EXAMPLE
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k^2 + k + 2 takes the values 2, 4, 8, 14, ... for k = 0,1,2,...; the smallest prime divisor of these numbers is 2, so f(2) = 2.
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CROSSREFS
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Cf. A060392-A060398. A060393 gives associated values of k.
Sequence in context: A107990 A117460 A136371 this_sequence A062608 A041791 A056720
Adjacent sequences: A060377 A060378 A060379 this_sequence A060381 A060382 A060383
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KEYWORD
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hard,nice,nonn
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AUTHOR
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Luis Rodriguez-Torres (ludovicusmagister(AT)yahoo.com), Apr 03 2001
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EXTENSIONS
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Corrected by T. D. Noe (noe(AT)sspectra.com), Apr 19 2004
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