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Search: id:A098036
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| A098036 |
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First occurrence of primes p such that p = (prime(k) + prime(k+n))/2 for some positive integer k and n=2, 3, ... |
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+0
1
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| 5, 7, 11, 59, 11, 13, 41, 17, 23, 43, 23, 29, 53, 31, 67, 53, 37, 59, 41, 43, 97, 53, 103, 53, 79, 59, 83, 149, 67, 167, 71, 127, 89, 113, 83, 89, 101, 149, 311, 97, 101, 109, 101, 107, 113, 127, 137, 131, 157, 137, 127, 149, 137, 163, 137, 281, 193, 149, 229, 191, 157
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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No primes exist for n=1, as (prime(k) + prime(k+1))/2 is between prime(k) and prime(k+1) and so cannot be prime. See the Weisstein link.
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LINKS
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Eric Weisstein's World of Mathematics, Interprime Numbers
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EXAMPLE
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For n=2, (prime(2) + prime(2+2))/2 = (3+7)/2 = 5, so a(2)=5.
For n=4, (prime(2) + prime(2+4))/2 = (3+13)/2 = 8, which is not prime, but (prime(3) + prime(3+4))/2 = (5+17)/2 = 11, so a(4)=11.
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PROGRAM
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(PARI) a(n) = {k=2; while(!isprime(p=(prime(k)+prime(k+n))/2), k++); p}
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CROSSREFS
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Sequence in context: A106819 A045968 A066367 this_sequence A127269 A071781 A091509
Adjacent sequences: A098033 A098034 A098035 this_sequence A098037 A098038 A098039
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KEYWORD
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easy,nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), Sep 10 2004
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EXTENSIONS
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Edited by Michael Porter (michael_b_porter(AT)yahoo.com), Oct 07 2009
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