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Search: id:A123914
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| A123914 |
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(Prime(n))^2 - prime(n^2). Commutator of (primes, squares) at n. |
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+0
1
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| 2, 2, 2, -4, 24, 18, 62, 50, 110, 300, 300, 542, 672, 656, 782, 1190, 1602, 1578, 2052, 2300, 2246, 2780, 3086, 3710, 4772, 5150, 5090, 5442, 5400, 5772, 8556, 9000, 10032, 9980, 12270, 12174, 13328, 14520, 15146, 16430, 17714, 17660, 20604, 20502, 21200
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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a(4) = -4 is the only negative value. All values are even. Asymptotically a(n) ~ (n log n)^2 - (n^2) log (n^2) = (n^2)*(log n)^2 - 2*(n^2)*(log n) = (n^2)*((log n)^2 - 2*log n) = O((n^2)*(log n)^2) which is the same as the asymptotic of commutator [primes,triangular numbers] at n, or, for that matter commutator [primes,k-gonal numbers] at n for any k>2.
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FORMULA
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a(n) = A001248(n) - A011757(n). a(n) = commutator [A000040,A000290] at n. a(n) = A000040(A000290(n)) - A000290(A000040(n)). a(n) = square(prime(n)) - prime(square(n)).
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EXAMPLE
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a(1) = (prime(1))^2 - prime(1^2) = prime(1)^2 - prime(1^2) = 4 - 2 = 2.
a(2) = (prime(2))^2 - prime(2^2) = prime(2)^2 - prime(2^2) = 9 - 7 = 2.
a(3) = (prime(3))^2 - prime(3^2) = prime(3)^2 - prime(3^2) = 25 - 23 = 2.
a(4) = (prime(4))^2 - prime(4^2) = prime(4)^2 - prime(4^2) = 49 - 53 = -4.
a(5) = (prime(5))^2 - prime(5^2) = prime(5)^2 - prime(5^2) = 121 - 97 = 24.
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MATHEMATICA
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f[n_] := Prime[n]^2 - Prime[n^2]; Array[f, 45] (* Robert G. Wilson v *)
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CROSSREFS
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Cf. A000040, A000290, A001248, A011757.
Adjacent sequences: A123911 A123912 A123913 this_sequence A123915 A123916 A123917
Sequence in context: A131562 A107902 A142974 this_sequence A088885 A121358 A112659
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KEYWORD
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easy,sign
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AUTHOR
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Jonathan Vos Post (jvospost2(AT)yahoo.com), Oct 28 2006
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EXTENSIONS
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More terms from Robert G. Wilson v Oct 29 2006
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