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A061066
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a(n) = (prime(n)^2 - 1)/8.
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3
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1, 3, 6, 15, 21, 36, 45, 66, 105, 120, 171, 210, 231, 276, 351, 435, 465, 561, 630, 666, 780, 861, 990, 1176, 1275, 1326, 1431, 1485, 1596, 2016, 2145, 2346, 2415, 2775, 2850, 3081, 3321, 3486, 3741, 4005, 4095, 4560, 4656, 4851, 4950, 5565, 6216, 6441
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OFFSET
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2,2
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COMMENTS
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This sequence is a subsequence of the triangular numbers (A000217) because (prime(n)^2-1)/8 = ((2m+1)^2-1)/8 = m(m+1)/2 where p=2m+1 for a given m. - David Morales Marciel, Oct 07 2015
The Jacobi symbol (2|p) = (-1)^((p^2-1)/8). - Michael Somos, Feb 17 2020
Number of inversions of the permutation ((2*i) mod p)_{1<=i<=p-1} = (2,4,...,p-1,1,3,...,p-2) of {1,2,...,p-1}, where p = prime(n). - Jianing Song, Apr 07 2023
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REFERENCES
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J. V. Uspensky and M. A. Heaslet, Elementary Number Theory, McGraw-Hill, NY, 1939, p. 307.
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LINKS
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FORMULA
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EXAMPLE
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a(2) = 1 because p = prime(2) = 3 and (3^2-1)/8 = 1. - Michael Somos, Feb 17 2020
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MATHEMATICA
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PROG
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(PARI) vector(100, n, (prime(n+1)^2 - 1)/8) \\ Altug Alkan, Oct 07 2015
(Magma) [(p^2-1)/8: p in PrimesInInterval(3, 300)]; // G. C. Greubel, May 03 2024
(SageMath) [(n^2-1)/8 for n in prime_range(3, 301)] # G. C. Greubel, May 03 2024
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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