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%I #38 May 04 2024 03:59:01
%S 1,3,6,15,21,36,45,66,105,120,171,210,231,276,351,435,465,561,630,666,
%T 780,861,990,1176,1275,1326,1431,1485,1596,2016,2145,2346,2415,2775,
%U 2850,3081,3321,3486,3741,4005,4095,4560,4656,4851,4950,5565,6216,6441
%N a(n) = (prime(n)^2 - 1)/8.
%C 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
%C The Jacobi symbol (2|p) = (-1)^((p^2-1)/8). - _Michael Somos_, Feb 17 2020
%C 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
%D J. V. Uspensky and M. A. Heaslet, Elementary Number Theory, McGraw-Hill, NY, 1939, p. 307.
%H Harvey P. Dale, <a href="/A061066/b061066.txt">Table of n, a(n) for n = 2..1000</a>
%F a(n) = A000217(A005097(n-1)). - after first comment, _Michel Marcus_, Oct 07 2015
%F a(n) = (3/8)*A024700(n-2). - _G. C. Greubel_, May 03 2024
%e a(2) = 1 because p = prime(2) = 3 and (3^2-1)/8 = 1. - _Michael Somos_, Feb 17 2020
%t f[n_]:=(Prime[n]^2-1)/8; Array[f,66,2] (* _Vladimir Joseph Stephan Orlovsky_, Aug 06 2009 *)
%t (#^2-1)/8&/@Prime[Range[2,50]] (* _Harvey P. Dale_, Nov 16 2012 *)
%o (PARI) vector(100, n, (prime(n+1)^2 - 1)/8) \\ _Altug Alkan_, Oct 07 2015
%o (Magma) [(p^2-1)/8: p in PrimesInInterval(3,300)]; // _G. C. Greubel_, May 03 2024
%o (SageMath) [(n^2-1)/8 for n in prime_range(3,301)] # _G. C. Greubel_, May 03 2024
%Y Cf. A000217, A005097, A024700.
%K nonn
%O 2,2
%A _Labos Elemer_, May 28 2001