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%I #26 May 15 2023 16:50:24
%S -1,-7,1,-23,73,49,217,193,217,721,553,1057,1513,1489,1609,2137,3241,
%T 2953,3937,4753,4417,5593,5857,6433,8617,9793,9769,11017,10993,9409,
%U 15097,15553,18217,16441,21601,20953,22729,25249,25849,27817,31321,29041,35713
%N a(n) = 2*prime(n)^2 - prime(n+1)^2.
%C Theorem: a(n) > 0 for all n > 4.
%D D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, 1996, Section VII.18, p. 247.
%H Harry J. Smith, <a href="/A064051/b064051.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = 2*A001248(n) - A001248(n+1). - _Elmo R. Oliveira_, Jan 13 2023
%t Table[2 Prime[n]^2 - Prime[n+1]^2, {n, 45}] (* _Vincenzo Librandi_, Jun 22 2018 *)
%t 2#[[1]]-#[[2]]&/@Partition[Prime[Range[50]]^2,2,1] (* _Harvey P. Dale_, May 15 2023 *)
%o (PARI) a(n) = 2*prime(n)^2 - prime(n + 1)^2; \\ _Harry J. Smith_, Sep 06 2009
%o (Magma) [2*NthPrime(n)^2 - NthPrime(n+1)^2: n in [1..45]]; // _Vincenzo Librandi_, Jun 22 2018
%Y Cf. A324798, A001248.
%K sign
%O 1,2
%A _N. J. A. Sloane_, Oct 15 2001
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