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Search: id:A100797
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| A100797 |
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For each n let n_2 be the smallest number bigger than n+1 and coprime to n*(n+1) and let n_3 be the smallest number bigger than n_2 and coprime to n*(n+1)*n_2. The sequence lists numbers n such that n*(n+1)+n_2*n_3 and -n*(n+1) + n_2*n_3 are prime. |
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| 1, 2, 3, 4, 5, 9, 11, 12, 15, 17, 19, 23, 26, 29, 30, 32, 33, 35, 43, 45, 61, 64, 71, 73, 75, 76, 83, 84, 85, 86, 90, 91, 95, 101, 107, 108, 110, 114, 121, 124, 132, 136, 137, 140, 142, 143, 163, 169, 175, 179, 182, 184, 198, 201, 211, 212, 219, 222, 223, 231, 234
(list; graph; listen)
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OFFSET
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1,2
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EXAMPLE
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Let n = 5: The smallest number bigger than 6 and coprime to 5*6 is 7. The smallest number bigger than 7 and coprime to 5*6*7 is 11. Therefore n_2 = 7 and n_3 = 11. Since 5*6 + 7*11 and -5*6 + 7*11 are both primes, 5 is an element of the sequence.
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MATHEMATICA
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e = {}; For[n = 1, n < 250, n++, a = n; b = n + 1; c = n + 2; While[Not[GCD[c, n]*GCD[c, n + 1] == 1], c++ ]; d = c + 1; While[Not[GCD[d, a]*GCD[d, b]*GCD[d, c] == 1], d++ ]; If[PrimeQ[a*b + c*d], If[PrimeQ[ - a*b + c*d], AppendTo[e, n]]]]; e
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CROSSREFS
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Sequence in context: A015837 A075177 A062096 this_sequence A139441 A093305 A065817
Adjacent sequences: A100794 A100795 A100796 this_sequence A100798 A100799 A100800
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KEYWORD
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nonn,less
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AUTHOR
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J. M. Bergot (thekingfishb(AT)yahoo.ca), May 26 2007
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EXTENSIONS
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Edited, corrected and extended by Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Nov 24 2007
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