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Search: id:A106545
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| A106545 |
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a(n) = n^2 if n^2 is the sum of two primes, otherwise a(n) = 0. |
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+0
3
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| 0, 4, 9, 16, 25, 36, 49, 64, 81, 100, 0, 144, 169, 196, 225, 256, 0, 324, 361, 400, 441, 484, 0, 576, 0, 676, 729, 784, 841, 900, 0, 1024, 1089, 1156, 1225, 1296, 1369, 1444, 0, 1600, 0, 1764, 1849, 1936, 0, 2116, 2209, 2304, 2401, 2500, 0, 2704, 0, 2916, 3025
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OFFSET
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1,2
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COMMENT
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For odd n, n^2 is odd so the two primes must be opposite in parity. Lesser prime must be 2 and greater prime must be n^2-2. Thus for odd n, n^2 is the sum of two primes iff n^2-2 is prime.
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FORMULA
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a(n) = n^2 - A106544(n).
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EXAMPLE
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a(2) = 2^2 = 4 = 2+2, a(5) = 5^2 = 25 = 23+2 (two primes).
a(1) = 0 because the sum of two primes is at least 4 and a(11) = 0 because 11^2 - 2 = 119 = 7*17 is composite.
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CROSSREFS
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Cf. A106544-A106548, A106562-A106564, A106571, A106573-A106575, A106577.
Sequence in context: A048387 A035121 A080151 this_sequence A093837 A069821 A000290
Adjacent sequences: A106542 A106543 A106544 this_sequence A106546 A106547 A106548
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KEYWORD
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easy,nonn
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AUTHOR
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Alexandre Wajnberg (alexandre.wajnberg(AT)ulb.ac.be), May 08 2005
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EXTENSIONS
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Edited and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de) and Ray Chandler (rayjchandler(AT)sbcglobal.net), May 12 2005
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